essay about charles law

November 16, 1998

What is Charles' law?

Balloon ascent by Charles, Prairie de Nesles, France, December 1783.

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Theodore G. Lindeman, professor and chair of the chemistry department of Colorado College in Colorado Springs, offers this explanation:

The physical principle known as Charles' law states that the volume of a gas equals a constant value multiplied by its temperature as measured on the Kelvin scale (zero Kelvin corresponds to -273.15 degrees Celsius).

The law's name honors the pioneer balloonist Jacques Charles, who in 1787 did experiments on how the volume of gases depended on temperature. The irony is that Charles never published the work for which he is remembered, nor was he the first or last to make this discovery. In fact, Guillaume Amontons had done the same sorts of experiments 100 years earlier, and it was Joseph Gay-Lussac in 1808 who made definitive measurements and published results showing that every gas he tested obeyed this generalization.

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It is pretty surprising that dozens of different substances should behave exactly alike, as these scientists found that various gases did. The accepted explanation, which James Clerk Maxwell put forward around 1860, is that the amount of space a gas occupies depends purely on the motion of the gas molecules. Under typical conditions, gas molecules are very far from their neighbors, and they are so small that their own bulk is negligible. They push outward on flasks or pistons or balloons simply by bouncing off those surfaces at high speed. Inside a helium balloon, about 10 24 (a million million million million) helium atoms smack into each square centimeter of rubber every second, at speeds of about a mile per second!

Both the speed and frequency with which the gas molecules ricochet off container walls depend on the temperature, which is why hotter gases either push harder against the walls (higher pressure) or occupy larger volumes (a few fast molecules can occupy the space of many slow molecules). Specifically, if we double the Kelvin temperature of a rigidly contained gas sample, the number of collisions per unit area per second increases by the square root of 2, and on average the momentum of those collisions increases by the square root of 2. So the net effect is that the pressure doubles if the container doesn't stretch, or the volume doubles if the container enlarges to keep the pressure from rising.

So we could say that Charles' Law describes how hot air balloons get light enough to lift off, and why a temperature inversion prevents convection currents in the atmosphere, and how a sample of gas can work as an absolute thermometer.

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and is called Charles' law . For this law to be valid, the pressure must be held constant , and the temperature must be expressed on the absolute temperature or Kelvin scale .

Because the volume of a gas decreases with falling temperature, scientists realized that a natural zero‐point for temperature could be defined as the temperature at which the volume of a gas theoretically becomes zero. At a temperature of absolute zero, the volume of an ideal gas would be zero. The absolute temperature scale was devised by the English physicist Kelvin, so temperatures on this scale are called Kelvin ( K ) temperatures. The relationship of the Kelvin scale to the common Celsius scale must be memorized by every chemistry student:

K = °C + 273.15

Therefore, at normal pressure, water freezes at 273.15 K (0°C), which is called the freezing point , and boils at 373.15 K (100°C). Room temperature is approximately 293 K (20°C). Both temperature scales are used in tables of chemical values, and many simple errors arise from not noticing which scale is presented.

Use Charles' law to calculate the final volume of a gas that occupies 400 ml at 20°C and is subsequently heated to 300°C. Begin by converting both temperatures to the absolute scale:

T 1 = 20°C = 293.15 K

T 2 = 300°C = 573.15 K

Then substitute them into the constant ratio of Charles' law:

When using Charles' law, remember that volume and Kelvin temperature vary directly; therefore, an increase in either requires a proportional increase in the other.

• A gas occupying 660 ml at a laboratory temperature of 20°C was refrigerated until it shrank to 125 ml. What is the temperature in degrees Celsius of the chilled gas?

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Charles's Law Definition in Chemistry

Charles Law Definition and Equation

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Charles's law is a gas law that states gases expand when heated. The law is also known as the law of volumes. The law takes its name from French scientist and inventor Jacques Charles, who formulated it in the 1780s.

Charles's Law Definition

Charles's Law is an ideal gas law where at constant pressure , the volume of an ideal gas is directly proportional to its absolute temperature . The simplest statement of the law is:

V/T = k

where V is volume, T is absolute temperature, and k is a constant V i /T i = V f /T f where V i = initial pressure T i = initial temperature V f = final pressure T f = final temperature

Charles's Law and Absolute Zero

If the law is taken to its natural conclusion, it appears the volume of a gas approaches zero and its temperature nears absolute zero . Gay-Lussac explained this could only be true if the gas continued to behave as an ideal gas, which it was not. Like other ideal gas laws, Charles's law works best when applied to gases under normal conditions.

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Gas Laws - Overview

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Created in the early 17th century, the gas laws have been around to assist scientists in finding volumes, amount, pressures and temperature when coming to matters of gas. The gas laws consist of three primary laws: Charles' Law, Boyle's Law and Avogadro's Law (all of which will later combine into the General Gas Equation and Ideal Gas Law).

Introduction

The three fundamental gas laws discover the relationship of pressure, temperature, volume and amount of gas. Boyle's Law tells us that the volume of gas increases as the pressure decreases. Charles' Law tells us that the volume of gas increases as the temperature increases. And Avogadro's Law tell us that the volume of gas increases as the amount of gas increases. The ideal gas law is the combination of the three simple gas laws.

Ideal Gases

Ideal gas, or perfect gas, is the theoretical substance that helps establish the relationship of four gas variables, p ressure (P) , volume (V) , the amount of gas (n) and temperature(T) . It has characters described as follow:

• The particles in the gas are extremely small, so the gas does not occupy any spaces.
• The ideal gas has constant, random and straight-line motion.
• No forces between the particles of the gas. Particles only collide elastically with each other and with the walls of container.

Real gas, in contrast, has real volume and the collision of the particles is not elastic, because there are attractive forces between particles. As a result, the volume of real gas is much larger than of the ideal gas, and the pressure of real gas is lower than of ideal gas. All real gases tend to perform ideal gas behavior at low pressure and relatively high temperature.

The compressibility factor (Z) tells us how much the real gases differ from ideal gas behavior.

\[ Z = \dfrac{PV}{nRT} \nonumber \]

For ideal gases, \( Z = 1 \). For real gases, \( Z\neq 1 \).

Boyle's Law

In 1662, Robert Boyle discovered the correlation between Pressure (P) and Volume (V) (assuming Temperature(T) and Amount of Gas(n) remain constant):

\[ P\propto \dfrac{1}{V} \rightarrow PV=x \nonumber \]

where x is a constant depending on amount of gas at a given temperature.

• Pressure is inversely proportional to Volume

Another form of the equation (assuming there are 2 sets of conditions, and setting both constants to eachother) that might help solve problems is:

\[ P_1V_1 = x = P_2V_2 \nonumber \]

Example \(\PageIndex{1}\)

A 17.50mL sample of gas is at 4.500 atm. What will be the volume if the pressure becomes 1.500 atm, with a fixed amount of gas and temperature?

\[ \begin{align*} V_2 &= \dfrac {P_1  V_1}{P_2} \\[4pt] &=\dfrac{4.500~ atm \cdot 17.50~mL}{1.500 ~atm} \\[4pt] &= 52.50~mL \end{align*} \]

Charles' Law

In 1787, French physicists Jacques Charles, discovered the correlation between Temperature(T) and Volume(V) (assuming Pressure (P) and Amount of Gas(n) remain constant):

\[ V \propto T \rightarrow V=yT \nonumber \]

where y is a constant depending on amount of gas and pressure. Volume is directly proportional to Temperature

Another form of the equation (assuming there are 2 sets of conditions, and setting both constants to each other) that might help solve problems is:

\[ \dfrac{V_1}{T_1} = y = \dfrac{V_2}{T_2} \nonumber \]

Example \(\PageIndex{2}\)

A sample of Carbon dioxide in a pump has volume of 20.5 mL and it is at 40.0 o C. When the amount of gas and pressure remain constant, find the new volume of Carbon dioxide in the pump if temperature is increased to 65.0 o C.

\[ \begin{align*} V_2&=\dfrac{V_1 \,T_2}{T_1} \\[4pt] &=\dfrac{20.5~mL (60+273.15~K)}{40+273.15~K} \\[4pt] &= 22.1~mL \end{align*} \]

Avogadro's Law

In 1811, Amedeo Avogadro fixed Gay-Lussac's issue in finding the correlation between the Amount of gas(n) and Volume(V) (assuming Temperature(T) and Pressure(P) remain constant):

\[ V \propto n \rightarrow V = zn \nonumber \]

where \(z\) is a constant depending on Pressure and Temperature.

• Volume (V) is directly proportional to the Amount of gas (n)

\[ \dfrac{P_1}{n_1} = z= \dfrac{P_2}{n_2} \nonumber \]

Example \(\PageIndex{3}\)

A 3.80 g of oxygen gas in a pump has volume of 150 mL. constant temperature and pressure. If 1.20g of oxygen gas is added into the pump. What will be the new volume of oxygen gas in the pump if temperature and pressure held constant?

V 1 =150 mL

\[ n_1= \dfrac{m_1}{M_{\text{oxygen gas}}} \nonumber \]

\[ n_2= \dfrac{m_2}{M_{\text{oxygen gas}}} \nonumber \]

\[ \begin{align*} V_2 &=\dfrac{V_1 \cdot n_2}{n_1} \\[4pt] &= \dfrac{150~mL \cdot \dfrac{5.00~g}{32.0~g \cdot mol^{-1}}} {\dfrac{3.80~g}{32.0~g \cdot mol^{-1}}} \\[4pt] &= 197~mL\end{align*} \]

Id e al Gas Law

The ideal gas law is the combination of the three simple gas laws. By setting all three laws directly or inversely proportional to Volume, you get:

\[ V \propto \dfrac{nT}{P} \nonumber \]

Next replacing the directly proportional to sign with a constant(R) you get:

\[ V = \dfrac{RnT}{P} \nonumber \]

And finally get the equation:

\[ PV = nRT \nonumber \]

where \(P\) is the absolute pressure of ideal gas

• \(V\) is the volume of ideal gas
• \(n\) is the amount of gas
• \(T\) is the absolute temperature
• \(R\) is the gas constant

Here, \(R\) is the called the gas constant . The value of \(R\) is determined by experimental results and its numerical value changes with units.

\[\begin{align} R &= 8.3145 ~J \cdot mol^{-1} \cdot K^{-1}~ \tag{in SI Units}  \\[4pt] &= 0.082057 ~L \cdot atm \cdot K^{-1} \cdot mol^{-1} \nonumber \end{align}\]

Example \(\PageIndex{5}\)

At 655 mmHg and 25.0  o C, a sample of Chlorine gas has volume of 750 mL. How many moles of chlorine gas at this condition?

• T=25+273.15 K
• V=750 mL=0.75L

\[\begin{align*} n &=\frac{PV}{RT} \\[4pt] &=\frac{655~mmHg \cdot \frac{1 ~atm}{760~mmHg} \cdot  0.75~L}{0.082057~L \cdot  atm \cdot mol^{-1} \cdot K^{-1} \cdot (25+273.15K) } \\[4pt] &=0.026~ mol \end{align*} \]

Evaluation of the Gas Constant, R

You can get the numerical value of gas constant, R, from the ideal gas equation, \(PV=nRT\). At standard temperature and pressure, where temperature is 0 o C, or 273.15 K, pressure is at 1 atm, and with a volume of \(22.4140~L\),

\[ \begin{align*} R &= \frac{PV}{nT} \\[4pt] &= \frac{1 ~atm \cdot 22.4140~L}{1 ~mol \cdot 273.15~K} \\[4pt] &=0.082057 \; L \cdot atm \cdot mol^{-1} K^{-1} \end{align*}\]

\[ \begin{align*} R &= \frac{PV}{nT} \\[4pt] &= \frac{1~ atm \cdot 2.24140 \times 10^{-2}~m^3}{1 ~mol \cdot 273.15~K} \\[4pt] &= 8.3145\; m^3\; Pa \cdot mol^{-1} \cdot K^{-1} \end{align*}\]

General Gas Equation

In an Ideal Gas situation, \( \frac{PV}{nRT} = 1 \) (assuming all gases are "ideal" or perfect). In cases where \( \frac{PV}{nRT} \neq 1 \) or if there are multiple sets of conditions (Pressure(P), Volume(V), number of gas(n), and Temperature(T)), use the General Gas Equation:

Assuming 2 set of conditions:

Initial Case: Final Case:

\[ P_iV_i = n_iRT_i \; \; \; \; \; \; P_fV_f = n_fRT_f \nonumber \]

Setting both sides to R (which is a constant with the same value in each case), one gets:

\[ R= \dfrac{P_iV_i}{n_iT_i} \; \; \; \; \; \; R= \dfrac{P_fV_f}{n_fT_f} \nonumber \]

If one substitutes one R for the other, one will get the final equation and the General Gas Equation:

\[ \dfrac{P_iV_i}{n_iT_i} = \dfrac{P_fV_f}{n_fT_f} \nonumber \]

Standard Conditions

If in any of the laws, a variable is not give, assume that it is given. For constant temperature, pressure and amount:

• Absolute Zero (Kelvin): 0 K = - 273.15 o C

T(K) = T( o C ) + 273.15 (unit of the temperature must be Kelvin)

2. Pressure: 1 Atmosphere (760 mmHg)

3. Amount: 1 mol = 22.4 Liter of gas

4. In the Ideal Gas Law, the gas constant R = 8.3145 Joules · mol -1 · K -1 = 0.082057 L · atm·K - 1 · mol - 1

The Van der Waals Equation For Real Gases

Dutch physicist Johannes Van Der Waals developed an equation for describing the deviation of real gases from the ideal gas. There are two correction terms added into the ideal gas equation. They are \( 1 +a\frac{n^2}{V^2}\), and \( 1/(V-nb) \).

Since the attractive forces between molecules do exist in real gases, the pressure of real gases is actually lower than of the ideal gas equation. This condition is considered in the van der Waals equation. Therefore, the correction term \( 1 +a\frac{n^2}{V^2} \) corrects the pressure of real gas for the effect of attractive forces between gas molecules.

Similarly, because gas molecules have volume, the volume of real gas is much larger than of the ideal gas, the correction term \(1 -nb \) is used for correcting the volume filled by gas molecules.

Exercise \(\PageIndex{1}\)

If 4L of H 2 gas at 1.43 atm is at standard temperature, and the pressure were to increase by a factor of 2/3, what is the final volume of the H 2 gas? (Hint: Boyle's Law)

To solve this question you need to use Boyle's Law:

\[ P_1V_1 = P_2V_2 \nonumber \]

Keeping the key variables in mind, temperature and the amount of gas is constant and therefore can be put aside, the only ones necessary are:

Plugging these values into the equation you get:

V 2 =(1.43atm x 4 L)/(2.39atm) = 2.38 L

• Final Volume(unknown): V 2

Exercise \(\PageIndex{2}\)

If 1.25L of gas exists at 35  o C with a constant pressure of .70 atm in a cylindrical block and the volume were to be multiplied by a factor of 3/5, what is the new temperature of the gas? (Hint: Charles's Law)

To solve this question you need to use Charles's Law:

\[\frac{V_1}{T_1}=\frac{V_2}{T_2} \nonumber \]

Once again keep the key variables in mind. The pressure remained constant and since the amount of gas is not mentioned, we assume it remains constant. Otherwise the key variables are:

Since we need to solve for the final temperature you can rearrange Charles's:

\[T_2=\frac{T_1 V_2}{V_1} \nonumber \] Once you plug in the numbers, you get: T 2 =(308.15 K x .75 L)/(1.25 L) = 184.89 K

• Final Temperature: T 2

Exercise \(\PageIndex{3}\)

A ballon with 4.00g of Helium gas has a volume of 500mL. When the temperature and pressure remain constant. What will be the new volume of Helium in the ballon if another 4.00g of Helium is added into the ballon? (Hint: Avogadro's Law)

Using Avogadro's Law to solve this problem, you can switch the equation into \( V_2=\frac{n_1\centerdot V_2}{n_2} \). However, you need to convert grams of Helium gas into moles.

\[ n_1 = \frac{4.00g}{4.00g/mol} = \text{1 mol} \nonumber \]

Similarly, n 2 =2 mol

\[ V_2=\frac{n_2 \centerdot V_2}{n_1} \nonumber \]

\[ =\frac{2 mol \centerdot 500mL}{1 mol} \nonumber \]

\[ = \text{1000 mL or 1L } \nonumber \] ​​​​

• Petrucci, Ralph H. General Chemistry: Principles and Modern Applications . 9th Ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2007.
• Staley, Dennis. Prentice Hall Chemistry . Boston, MA: Pearson Prentice Hall, 2007.
• Olander, Donald R. "Chapter2 Equation of State." General Thermodynamics . Boca Raton, NW: CRC, 2008. Print
• O'Connell, John P., and J. M. Haile. "Properties Relative to Ideal Gases." Thermodynamics: Fundamentals for Applications . Cambridge: Cambridge UP, 2005. Print.
• Ghare, Shakuntala. "Ideal Gas Laws for One Component." Ideal Gas Law, Enthalpy, Heat Capacity, Heats of Solution and Mixing . Vol. 4. New York, NY, 1984. Print. F.

• Chemistry Formulas

Charles Law Formula

What is charles law.

Charles’ law is one of the gas laws which explains the relationship between volume and temperature of a gas. It states that when pressure is held constant, the volume of a fixed amount of dry gas is directly proportional to its absolute temperature. When two measurements are in direct proportion then any change made in one of them affects the other through direct variation. Charles’ Law is expressed by the equation:

\(\begin{array}{l}V\alpha T\end{array} \)

\(\begin{array}{l}\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}\end{array} \)

Where, V 1 and V 2 are the Initial Volumes and Final Volume respectively. T 1 refers to the Initial Temperature and T 2 refers to the Final Temperature. Both the temperatures are in the units of Kelvin.

Jacques Charles, a French scientist, in 1787, discovered that keeping the pressure constant, the volume of a gas varies on changing its temperature. Later, Joseph Gay-Lussac, in 1802, modified and generalized the concept as Charles’s law. At very high temperatures and low pressures, gases obey Charles’ law.

Derivation:

Charles’ Law states that at constant pressure, the volume of a fixed mass of a dry gas is directly proportional to its absolute temperature. We can represent this using the following equation:

Since V and T vary directly, we can equate them by making use of a constant k.

\(\begin{array}{l}\frac{V}{T}=constant=k\end{array} \)

Let V 1  and T 1  be the initial volume and temperature of an ideal gas. We can write equation I as:

\(\begin{array}{l}\frac{V_{1}}{T_{1}}=k\end{array} \) ———– (I)

Let’s change the temperature of the gas to T 2. Consequently, its volume changes to V 2 . So we can write,

\(\begin{array}{l}\frac{V_{2}}{T_{2}}=k\end{array} \) ———– (II)

Equating equations (II) and (III),

\(\begin{array}{l}\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}=k\end{array} \)

Hence, we can generalize the formula and write it as:

\(\begin{array}{l}\frac{(V_{1})}{(T_{1})}=\frac{(V_{2})}{(T_{2})}\end{array} \)

\(\begin{array}{l}V_{1}T_{2}=V_{2}T_{1}\end{array} \)

You know that on heating up a fixed mass of gas, that is, increasing the temperature, the volume also increases. Similarly, on cooling, the volume of the gas decreases. 

It is to be noted here that the unit Kelvin is preferred for solving problems related to Charles’ Law, and not Celsius . Kelvin (T) is also known as the Absolute temperature scale. For converting temperature to Kelvin scale, you add 273 to the temperature in the centigrade/Celsius scale.

Charles’ Law in Real Life:

Charles’ law has a wide range of applications in our daily life. Some of the common examples are given below:

• In cold weather or environment, balls and helium balloons shrink.
• In bright sunlight, the inner tubes swell up.
• In colder weather, the human lung capacity will also decrease. This makes it more difficult to do jogging or athletes to perform on a freezing winter day.

Solved Examples

Question 1:

  A gas occupies a volume of 400cm 3     at 0 °C and 780 mm Hg. What volume (in litres) will it occupy at 80 °C  and 780 mm Hg?

Solution: Given,

V 1 = 400 cm³  V 2 =? T 1 = 0°C = 0+273 = 273 K T 2 = 80°C = 80+273 = 353 K

Here the pressure is constant and only the temperature is changed.

Using Charles Law,

\(\begin{array}{l}\frac{400}{273}=\frac{V_{2}}{353}\end{array} \)

\(\begin{array}{l}V_{2}=\frac{400\times 353}{273}\end{array} \)

\(\begin{array}{l}V_{2}=517.21cm^{3}\end{array} \)

1 cubic centimeter = 0.001 litre =1 x 10 -3 litre

∴ 517.21 cubic centimeter = 517.21 x 10 -3 = 0.517 litres

Question 2:

Find the initial volume of a gas at 150 K, if the final volume is 6 L at 100 K

V 1 =?  V 2 =6 L T 1 = 150 K

T 2 = 100 K

\(\begin{array}{l}\frac{(V_{1})}{(150)}=\frac{(6)}{(100)}\end{array} \)

\(\begin{array}{l}V_{1}=\frac{6\times 150}{100}\end{array} \)

\(\begin{array}{l}V_{1}=9L\end{array} \)

The initial volume of a gas at 150 K is 9 litres.

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Home » Top 6 » Thermodynamics Applications » 10 Charles Law Examples in Real Life

10 Charles Law Examples in Real Life

Wanna know what are the top 10 Examples of Charles Law in Real Life? If yes, then you are at the right place at the very right time. Charles Law is an Ideal Gas Law that establishes a relation between volume and temperature at constant pressure.

In other words, according to Charles’s law definition; the volume of a gas increases with an increase in temperature at constant pressure and vice versa. Jaques Charles’s law is also known as the Law Of Volumes.

Related, Boyle’s Law – The Law Of Constant Temperature

This phenomenon was demonstrated by French Scientist, Inventor, and Mathematician Jacques Charles who first proposed this law in his unpublished work in the 1780s.

Charles Law Examples in Real Life

Hot air balloon.

• Bursting of a Deodorant

Bakery Products

Turkey pop-up timer, opening of a soda can.

• Helium Balloon on Cold Day

People often ask questions like – how do hot air balloons fly? Or how do hot air balloons work? Any guesses!!! Of course, whatever you are thinking it’s correct. The answers to all these questions lie in the vicinity of Charles Law.

In fact, if I talk about the history of hot air ballooning, Charles’s law and hot air balloons are somehow related. In other words, Jacques Charles himself was one of the famous hot-air balloonists.

He was notably one of the few people who flew the world’s first hydrogen balloon flight. The principle behind the working of a hot air balloon is quite simple.

Parts of a hot air balloon basically consist of an Envelope that stores heated air, a Burner, and a Basket or Gondola to carry passengers.

When the fuel source is ignited, the air inside the envelope gets heated. Charles’s Law states that with an increase in the temperature of the air, the volume of the air will also increase.

Therefore, as a result, the density of air contained in an envelope becomes lighter than the density of the outside atmosphere. Hence, due to buoyant force , a hot air balloon flies high; up in the sky.

Bursting of a Deodorant Bottle

Well, in today’s world, we all are well aware of the fact of what deodorants are. And why are they being used? I also wonder how many of us get a chance to read the instructions written as warning signs such as a ” pressurized container, protect it from sunlight. Do not expose to temperature exceeding 50°C”.

Check out the latest Top 6 Applications Of Gay-Lussac’s Law

Ever thought about why? Well yes, your guess is correct. It’s because of Charle’s Law. According to Charles’s law definition; under high temperatures, the gas molecules inside the deodorant bottle expand. Therefore, leads to the bursting of the deodorant bottle…!!!

If you love bakery products like bread and cakes, you can thank Jacques Charles. Charles Law’s application in real life can be seen in our kitchen too. In order to make bread and cakes soft and spongy, yeast is used for fermentation.

Recommended, Top 6 Real-Life Applications of Boyle’s Law

Yeast produces carbon dioxide gas. When bread and cakes are baked at high temperatures; with an increase in temperature, carbon dioxide gas expands.

As a result of this expansion, our bread, and cakes become deliciously spongy and fluffy in appearance and ready to serve.

As I said, there are numerous applications of Charles law in our kitchen too. The working of the Turkey Pop-Up Timer is based on Charles’s Law Of Thermodynamics .

As it states that a gas tends to expand when heated”, the same phenomenon works for the Pop Up Turkey Thermometer. The turkey thermometer is placed inside the turkey.

Check out the  Top 6 Most Common Examples of Condensation

As the turkey cooks, the gas inside the thermometer expands with an increase in temperature. Therefore, the turkey thermometer pops up; indicating that the turkey is cooked and ready to serve.

Have you ever wondered why when you open a chilled soda can, you hardly see any bubbles? On the contrary, when you open a warm enough soda can, bubbles spill out of the drink. Any idea why? Yup, you are right. It happens because of the Charles Law Of Thermodynamics.

Must read, Gay Lussac’s Law – The Law Of Constant Volume 

According to Charles’s law definition, in a chilled soda can, due to low temperature, there is a decrease in the volume. That’s why you hardly see any bubbles coming out of the soda can.

On the other hand, in a warmer soda can, due to the high temperature, there is an increase in the volume. That’s why bubbles spill out of the drink.

Helium Ballon on Cold Day

Well, everyone is quite aware of what a helium balloon is. We all remember that during our childhood days when we stepped outside our home with a helium balloon on chilly days (winter season of course).

Editor’s Choice:  Dalton’s Law – The Law of Partial Pressure

The balloon will shrink a bit due to the degree of coldness or decrease in temperature. It happens because of Charles’s gas Law.

According to Charles’s law definition; when the temperature decreases so does the volume of helium gas inside a balloon. On the other hand, when the same balloon is brought back to a worm room, it regains its original shape.

Some Other Real Life Charles Law Examples

Apart from the above-mentioned ones, I am also mentioning a few here.

• Ping-Pong Ball
• Working of Engine, etc.

You might also like:

• Top 6 Verified Examples of Evaporation in Daily Life
• Top 6 Exclusive Sublimation Examples in Daily Life
• Sublimation Definition, Process, Facts & Examples

I am a mechanical engineer by profession. Just because of my love for fundamental physics, I switched my career, and therefore I did my postgraduate degree in physics. Right now I am a loner (as ever) and a Physics blogger too. My sole future goal is to do a Ph.D. in theoretical physics, especially in the field of cosmology. Because in my view, every aspect of physics comes within the range of cosmology. And I love traveling, especially the Sole one.

9 thoughts on “10 Charles Law Examples in Real Life”

NICE AND INFORMATIVE ARTICLE

Thankyou so much for your support. Hope to see you more frequent on my blog.

Thank you so much for your wonderful explanation of the applications of Charles law…

Great informative about real life application of Charles’s law

Thnx Ethan. Keep visiting us!!!

this is great!!

thanx, keep visiting us…!!!

Is there Boyle’s Law

Of course, there is Boyle’s law. I am attaching the link to Boyle’s law applications in real life for your further reading. Keep visiting us…!!! 6 Boyle’s Law Applications in Real Life (All New)

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Charles' law

Charles' law (also known as the law of volumes) is an experimental gas law which describes how gases tend to expand when heated. A modern statement of Charles' law is:

When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be directly related.[1]

this directly proportional relationship can be written as:

\( V \propto T\, \)

\( \frac{V}{T}=k \)

V is the volume of the gas T is the temperature of the gas (measured in Kelvin). k is a constant.

This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. For comparing the same substance under two different sets of conditions, the law can be written as:

\( \frac{V_1}{T_1} = \frac{V_2}{T_2} \qquad \mathrm{or} \qquad \frac {V_2}{V_1} = \frac{T_2}{T_1} \qquad \mathrm{or} \qquad V_1 T_2 = V_2 T_1. \)

The equation shows that, as absolute temperature increases, the volume of the gas also increases in proportion.

Discovery and naming of the law

The law was named after scientist Jacques Charles, who formulated the original law in his unpublished work from the 1780s. In two of a series of four essays presented between 2 and 30 October 1801,[2] John Dalton demonstrated by experiment that all the gases and vapours that he studied, expanded by the same amount between two fixed points of temperature. The French natural philosopher Joseph Louis Gay-Lussac confirmed the discovery in a presentation to the French National Institute on 31 Jan 1802,[3] although he credited the discovery to unpublished work from the 1780s by Jacques Charles. The basic principles had already been described a century earlier by Guillaume Amontons[4] and Francis Hauksbee.[5]

Dalton was the first to demonstrate that the law applied generally to all gases, and to the vapours of volatile liquids if the temperature was well above the boiling point. Gay-Lussac concurred.[6] With measurements only at the two thermometric fixed points of water, Gay-Lussac was unable to show that the equation relating volume to temperature was a linear function. On mathematical grounds alone, Gay-Lussac's paper does not permit the assignment of any law stating the linear relation. Both Dalton's and Gay-Lussac's main conclusions can be expressed mathematically as:

\( V_{100} - V_0 = kV_0\, \)

where V100 is the volume occupied by a given sample of gas at 100 °C; V0 is the volume occupied by the same sample of gas at 0 °C; and k is a constant which is the same for all gases at constant pressure. This equation does not contain the temperature and so has nothing to do with what became known as Charles' Law. Gay-Lussac's value for “k” (1⁄2.6666), was identical to Dalton's earlier value for vapours and remarkably close to the present-day value of 1⁄2.7315. Gay-Lussac gave credit for this equation to unpublished statements by his fellow Republican citizen J. Charles in 1787. In the absence of a firm record, the gas law relating volume to temperature cannot be named after Charles. Dalton's measurements had much more scope regarding temperature than Gay-Lussac, not only measuring the volume at the fixed points of water, but also at two intermediate points. Unaware of the inaccuracies of mercury thermometers at the time, which were divided into equal portions between the fixed points, Dalton, after concluding in Essay II that in the case of vapours, “any elastic fluid expands nearly in a uniform manner into 1370 or 1380 parts by 180 degrees (Fahrenheit) of heat”, was unable to confirm it for gases. His conclusion for vapours is a clear statement of what became become known wrongly as Charles' Law, then even more wrongly as Gay-Lussaac's law, but never correctly as Dalton's 2nd law. His 1st law was that of partial pressures.

Relation to absolute zero

Charles' law appears to imply that the volume of a gas will descend to zero at a certain temperature (−266.66 °C according to Gay-Lussac's figures) or −273.15 °C. Gay-Lussac was clear in his description that the law was not applicable at low temperatures:

but I may mention that this last conclusion cannot be true except so long as the compressed vapors remain entirely in the elastic state; and this requires that their temperature shall be sufficiently elevated to enable them to resist the pressure which tends to make them assume the liquid state.[3]

Gay-Lussac had no experience of liquid air (first prepared in 1877), although he appears to believe (as did Dalton) that the "permanent gases" such as air and hydrogen could be liquified. Gay-Lussac had also worked with the vapours of volatile liquids in demonstrating Charles' law, and was aware that the law does not apply just above the boiling point of the liquid:

I may however remark that when the temperature of the ether is only a little above its boiling point, its condensation is a little more rapid than that of atmospheric air. This fact is related to a phenomenon which is exhibited by a great many bodies when passing from the liquid to the solid state, but which is no longer sensible at temperatures a few degrees above that at which the transition occurs.[3]

The first mention of a temperature at which the volume of a gas might descend to zero was by William Thomson (later known as Lord Kelvin) in 1848:[7]

This is what we might anticipate, when we reflect that infinite cold must correspond to a finite number of degrees of the air-thermometer below zero; since if we push the strict principle of graduation, stated above, sufficiently far, we should arrive at a point corresponding to the volume of air being reduced to nothing, which would be marked as −273° of the scale (−100/.366, if .366 be the coefficient of expansion); and therefore −273° of the air-thermometer is a point which cannot be reached at any finite temperature, however low.

However, the "absolute zero" on the Kelvin temperature scale was originally defined in terms of the second law of thermodynamics, which Thomson himself described in 1852.[8] Thomson did not assume that this was equal to the "zero-volume point" of Charles' law, merely that Charles' law provided the minimum temperature which could be attained. The two can be shown to be equivalent by Ludwig Boltzmann's statistical view of entropy (1870).

However, Charles also stated:

The volume of a fixed mass of dry gas increases or decreases by 1/273 times the volume at 0oC for every 1o rise or fall in temperature. Thus-

\( V_t=V_0+(1/273\times V_0 )\times t \)

\( V_t=V_0 (1+t/273) \)

Where Vt is the volume of gas at temperature t, V0 is the volume at 0oC. Relation to kinetic theory

The kinetic theory of gases relates the macroscopic properties of gases, such as pressure and volume, to the microscopic properties of the molecules which make up the gas, particularly the mass and speed of the molecules. In order to derive Charles' law from kinetic theory, it is necessary to have a microscopic definition of temperature: this can be conveniently taken as the temperature being proportional to the average kinetic energy of the gas molecules, Ek:

\( T \propto \bar{E_{\rm k}}.\, \)

Under this definition, the demonstration of Charles' law is almost trivial. The kinetic theory equivalent of the ideal gas law relates pV to the average kinetic energy:

\( pV = \frac{2}{3} N \bar{E_{\rm k}}\, \)

See also Portal icon Underwater diving portal

Boyle's law Combined gas law Gay-Lussac's law Avogadro's law Ideal gas law Hand boiler

Fullick, P. (1994), Physics, Heinemann, pp. 141–42, ISBN 0-435-57078-1. J. Dalton (1802) "Essay II. On the force of steam or vapour from water and various other liquids, both in vacuum and in air" and Essay IV. "On the expansion of elastic fluids by heat," Memoirs of the Literary and Philosophical Society of Manchester, vol. 5, pt. 2, pages 550-574 and pages 595–602 . Gay-Lussac, J. L. (1802), "Recherches sur la dilatation des gaz et des vapeurs" [Researches on the expansion of gases and vapors], Annales de chimie 43: 137–175. English translation (extract). On page 157, Gay-Lussac mentions the unpublished findings of Charles: "Avant d'aller plus loin, je dois prévenir que quoique j'eusse reconnu un grand nombre de fois que les gaz oxigène, azote, hydrogène et acide carbonique, et l'air atmosphérique se dilatent également depuis 0° jusqu'a 80°, le cit. Charles avait remarqué depuis 15 ans la même propriété dans ces gaz ; mais n'avant jamais publié ses résultats, c'est par le plus grand hasard que je les ai connus." (Before going further, I should inform [you] that although I had recognized many times that the gases oxygen, nitrogen, hydrogen, and carbonic acid [i.e., carbon dioxide], and atmospheric air also expand from 0° to 80°, citizen Charles had noticed 15 years ago the same property in these gases; but having never published his results, it is by the merest chance that I knew of them.) See:

Amontons, G. (presented 1699, published 1732) "Moyens de substituer commodément l'action du feu à la force des hommes et des chevaux pour mouvoir les machines" (Ways to conveniently substitute the action of fire for the force of men and horses in order to power machines), Mémoires de l’Académie des sciences de Paris (presented 1699, published 1732), 112–126; see especially pages 113–117. Amontons, G. (presented 1702, published 1743) "Discours sur quelques propriétés de l'Air, & le moyen d'en connoître la température dans tous les climats de la Terre" (Discourse on some properties of air and on the means of knowing the temperature in all climates of the Earth), Mémoires de l’Académie des sciences de Paris, 155–174. Review of Amontons' findings: "Sur une nouvelle proprieté de l'air, et une nouvelle construction de Thermométre" (On a new property of the air and a new construction of thermometer), Histoire de l'Academie royale des sciences, 1–8 (submitted: 1702 ; published: 1743).

Englishman Francis Hauksbee (1660–1713) independently also discovered Charles' law: Francis Hauksbee (1708) "An account of an experiment touching the different densities of air, from the greatest natural heat to the greatest natural cold in this climate," Philosophical Transactions of the Royal Society of London 26(315): 93–96.

Gay-Lussac (1802), from page 166: "Si l'on divise l'augmentation totale de volume par le nombre de degrés qui l'ont produite ou par 80, on trouvera, en faisant le volume à la température 0 égal à l'unité, que l'augmentation de volume pour chaque degré est de 1 / 223.33 ou bien de 1 / 266.66 pour chaque degré du thermomètre centrigrade." If one divides the total increase in volume by the number of degrees that produce it or by 80, one will find, by making the volume at the temperature 0 equal to unity (1), that the increase in volume for each degree is 1 / 223.33 or 1 / 266.66 for each degree of the centigrade thermometer. From page 174: " … elle nous porte, par conséquent, à conclure que tous les gaz et toutes les vapeurs se dilatent également par les mêmes degrés de chaleur." … it leads us, consequently, to conclude that all gases and all vapors expand equally [when subjected to] the same degrees of heat. Thomson, William (1848), "On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive Power of Heat, and calculated from Regnault's Observations", Philosophical Magazine: 100–6.

Thomson, William (1852), "On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam", Philosophical Magazine 4. Extract.

Further reading

Krönig, A. (1856), "Grundzüge einer Theorie der Gase", Annalen der Physik 99: 315–22, Bibcode:1856AnP...175..315K, doi:10.1002/andp.18561751008. Facsimile at the Bibliothèque nationale de France (pp. 315–22). Clausius, R. (1857), "Ueber die Art der Bewegung, welche wir Wärme nennen", Annalen der Physik und Chemie 176: 353–79, Bibcode:1857AnP...176..353C, doi:10.1002/andp.18571760302. Facsimile at the Bibliothèque nationale de France (pp. 353–79). Joseph Louis Gay-Lussac – Liste de ses communications[dead link]. (French)

Physics Encyclopedia

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Charles Reich’s Unruly Administrative State

abstract. This Essay considers Charles Reich’s legacy in administrative law. It contends that Reich’s work was crucial in establishing microlevel administrative law, which provides a legal framework for an individual’s encounters with the state. I outline three aspects of microlevel administrative law that Reich inspired: the claim that microlevel administrative law should be understood through the “spaces” of the administrative state, the claim that microlevel administrative law invokes a broad range of values, and the claim that administrative law should consider the social and political vulnerability of the individual in encounters with the state.

Charles Reich’s notoriety in administrative law derives from the important claim undergirding his seminal work The New Property 1 :certain procedural 2 and constitutional rights 3 should accompany the removal of entitlements. He termed these entitlements “the new property” and viewed them as arising from government-created “wealth,” including income and other benefits, jobs, occupational licenses, franchises, contracts, subsidies, use of public resources, and services. 4 In Goldberg v. Kelly , 5 the Supreme Court cited Reich’s theory of new property entitlements with approval, and since then, Reichian entitlement theory—its ongoing vitality 6 and, more controversially, its decline—has been a key area of debate in administrative-law scholarship. 7

We would, however, profoundly understate the impact of Reich’s scholarship if we focused solely on his contribution to entitlement theory. Reich’s legacy in administrative law stems also from his exploration of individuality within the administrative state. When it comes to this latter contribution, the closest analogue to Reich is not another legal scholar; rather it is the noted documentarian Frederick Wiseman, who has studied the daily interactions of individuals in such institutional spaces as mental hospitals, libraries, universities, high schools, and public housing. Richard Brody spoke of Wiseman’s documentary film Welfare 8 in terms that would have equally applied to Reich’s work: “[w] hat makes it not merely smart but profoundly moving is his alertness to the tension between the order of institutions—which, after all, is a key form of social glue—and the unruly, passionate, authentic needs and desires of individuals.” 9

Reich’s scholarly contribution to administrative law, exemplified by his trilogy of articles written in the 1960s— Midnight Welfare Searches and the Social Security Act , 10 The New Property , 11 and Individual Rights and Social Welfare: The Emerging Legal Issues 12 —arises, much like Wiseman’s contribution, from this desire to engage with the often unruly relations of individuals and institutions and the law’s intervention in those relations. Reich’s focus on individual encounters with the state offers a new way of understanding what I term “ microlevel administrative law.” Microlevel administrative law is interested in how the law shapes an individual’s encounters with agencies of the administrative state. 13 Microlevel administrative law differs from the bulk of administrative law—which concerns itself with examining macrolevel relationships between agencies and the legislative, executive, and judicial branches of government—in three key ways.

First, Reich identified spatiality —the actual interactions between an administrator and an individual in a particular space 14 —as key to the assessment of microlevel administrative law.He examined a series of spaces—the automobile, 15 the home, 16 and the highway 17 —and explored the changing ways in which the law mediated the experience of those spaces. For example, Reich thought of welfare inspections as raiding the “space” of the home and analyzed questions about the scope of civil searches under the Fourth Amendment (including the ability of a welfare recipient to consent to such a search, the use of criminal process against a welfare recipient, and the reasonableness of welfare searches) with that spatial sensitivity. As Sarah Seo observes in her penetrating treatment of Reich’s use of the space of the “automobile” to frame the individual’s systematic encounters with the state, Reich’s work reveals “how the due-process revolution in criminal procedure emerged from the same set of historical circumstances that made due-process rights essential to preserving individual liberty in the regulatory state.” 18

Reich’s insight into administrative spatiality was, and still is, radical because it takes a systematic approach to an individual’s experience with the state. An individual, according to Reich, does not experience the state in an administrative-law silo or a criminal-law silo. Rather, an individual’s experience with the state might be a mix of shifting and often casual encounters shaped by the space in which these encounters take place.

The sidelining of Reich’s perspective in administrative spatiality has left the field largely unresponsive to events that should have significance for administrative law. For example, the Department of Justice’s investigation of Ferguson, Missouri is not often discussed as an administrative-law moment. 19 This changes, however, if we see that the Department of Justice, by focusing on the space of that “town,” provided a unifying lens by which to view how an individual encounters the state in two key ways. First, in a way similar to the welfare home raid Reich described, the Report uses the space of the “town” to emphasize how the state —exemplified by a systematic matrix of police and administrative actions—captured individuals in a web of civic surveillance that eroded community trust and caused significant social conflict. 20 Second, the Report focuses on the space of the “town” to reveal how intersections between different areas of law may have a cumulative impact on how a person’s encounters with the state may shape their ideas of its political legitimacy. ​ Namely, the more fraught encounters a person has with the state may make it less likely that the person may be less likely to view the state as a political legitimate actor. Thus, spatiality performs an integrative function in administrative law by providing a richer context for understanding an individual’s encounters with the state.

Our discussions of the state’s administrative legitimacy often focus on the structural relationships between agencies and their supervising forces, such as judicial review. 21 Reich showed that an agency’s legitimacy is also shaped by citizens’ experiential encounters with the state. A Reichian perspective, consequently, suggests a number of analytic innovations. For example, an interdisciplinary approach to administrative law grounded in anthropology may be just as useful as one grounded in political science. 22 Or, administrative law scholarship may map an individual’s dynamic, shifting relationships to multiple local, regional, and federal authoritative entities within a given regulatory regime. 23

Second, Reich’s microlevel approach generated the insight that individual interactions with the stateimplicate more than one constitutional value. By focusing on Reich’s arguments about procedural fairness, we have ignored Reich’s insight that microlevel administrative actions raise other constitutional issues as well, including privacy, equality, and dignity. In Individual Rights and Social Welfare , for instance, Reich argued for two other constitutional values in addition to fair agency procedures: equal protection under the law and privacy owed to a welfare recipient by the state. 24 Reich challenged the idea that welfare recipients should be treated differently because they receive benefits:

[A] nother developing constitutional problem is the degree to which it is valid to impose different standards of behavior upon people because they happen to receive some form of public assistance . . . . [T]he status of being a welfare beneficiary does not necessarily justify all of the differential forms of treatment which now exist under the law. 25

Likewise, a welfare recipient should enjoy a liberty interest in the “management of personal and family affairs—the sort of things that are, to the average person, nobody else’s business, certainly not government’s,” and an associated right to privacy “centering on home and family.” 26

Reich’s perspective has proven to be a durable one. In the context of equal-protection law, Reich’s perspective highlights the constitutional debates that are emerging over states’ ability to tie “work” requirements to healthcare benefits. 27 Additionally, Reich’s claim that welfare recipients deserve privacy in their interactions with the state has proven to be remarkably prescient. Virginia Eubanks, in Digital Dead End: Fighting for Social Justice in the Information Age , describes the techno-political experiences of working-class women on public assistance and their need for greater privacy in words that harken back to Reich:

The rapid sharing of database information between agencies lends credence to clients’ fears that they are trapped in a system where every detail of their lives is known and freely shared among powerful players: caseworkers, employers, politicians, and police. Rules for information gathering, sharing, and retrieval are obscure, and mechanisms ensuring accountability are rare. 28

Reich’s recognition of the centrality of constitutional values, such as equal protection and privacy, to microlevel administrative action points administrative-law scholars in some directions in which they already have been going: an increased appreciation for agencies’ role in advancing and implementing constitutional claims related, for instance, to equal-protection claims under the Fourteenth Amendment. 29 It also points to other directions in which administrative law should go, such as asking how social movements create their own popular conceptions of administrative action and interpretation insofar as such movements necessarily invoke a range of social values that lie outside of those movements’ technical understanding and legal claims. 30

Third and finally, Reich’s insight into microlevel administrative actions is grounded in an understanding of the expressive power of such actions for an individual. This is the experientialelement of administrative law. Reich appears to have been aware that individuals’ preexisting social and political vulnerabilities shape their microlevel administrative interactions. For instance, Reich was concerned about midnight welfare searches because “persons on welfare are mostly unable to protect their own rights” 31 given that they “are often ignorant of their rights, lack adequate representation by counsel, and lack the resources to fight a large public agency.” 32

Reich understood that individuals’ encounters with the state are shaped by class, race, gender, sexual orientation, and other markers of social identity. Take, for instance, a subject that clearly sparked Reich’s interests: the encounter of African American women with the supervisory welfare state. 33 African American women, at the time, were uniquely harmed by the intrusive searches of welfare recipients and, as Priscilla Ocen 34 has described, “[t]he racial profiling of Black women’s bodies through social welfare programs such as Section 8” continues today and thus demonstrates that “the intersection of race, gender, and class is essential to . . . the maintenance of racial segregation and the burgeoning punitive welfare state.” 35 Thus, Reich’s conception of the administrative subject incorporates a claim that administrative law as a field needs to have the capacity to see, and more importantly, to validate the claim that not all administrative subjects stand before the state in an equal manner. Goldberg v. Kelly is often cited for its recognition of welfare as an entitlement. But it should at least as often be cited for its broader recognition that “[t]he opportunity to be heard must be tailored to thecapacities and circumstances of those who are to be heard.” 36

Reich’s sensitivity to the political vulnerability of welfare recipients may have been a consequence of his comfort with the intersection of law and sociology, as a matter of practice and as a matter of method. As a matter of practice, as Martha Davis has emphasized, Reich produced his work in conversation with activists, administrators, and lawyers who sought to reform poverty law. As a matter of method, Reich used a variety of interdisciplinary sociological studies to buttress his theoretical claims. This interdisciplinary turn was not new; the field of poverty law was already firmly interdisciplinary in its approach. 37 But Reich’s insight into the situational vulnerability experienced by individuals in their interactions with the state has resonated in other disciplines such as civil-rights law. For instance, Atiba Ellis, studying the procedural due-process burdens associated with recent voter-identification laws, contends that such analysis should take into account “the intersecting vulnerabilities that poor people of color suffer from within the political and economic process. Such vulnerability lies at the heart of both the historical and present day-discrimination within the franchise (and the structures that affect it).” 38 Ellis’s useful focus on vulnerability is often absent in mainstream administrative-law teaching and scholarship. Reviving Reich’s situational insight into the vulnerabilities of individuals in particular spaces offers a way to successfully place individuals’ vulnerability at the center of administrative law.

Reich’s legacy in administrative law is often reduced to his linking of procedural due-process claims to entitlements and his consequent influence on Goldberg v. Kelly .This is a mistake because the unruly richness of Reich’s broader vision can teach us many more lessons today. In a political environment charged with questions of inequality, Reich’s insights into microlevel administrative law—analyzing administrative spaces to capture the ways in which cross-cutting legal regimes can have a cumulative effect on an individual, highlighting the diverse constitutional regimes that might impact the individual’s encounters with the state, and situating the individual’s social and political vulnerabilities as she encounters the state—continue to offer a valuable way to interrogate the relationship of the state to its citizenry.

Professor of Law, Marquette University Law School. I would like to thank Azene Seidoffini for her assistance on this fast-moving project.

Announcing the Eighth Annual Student Essay Competition

Announcing the ylj academic summer grants program, announcing the editors of volume 134, this essay is part of a collection, a tribute to charles reich.

Charles Reich—a beloved law professor, writer, and visionary—passed away on June 15, 2019. This Collection explores his rich life and legacy in the law and shares some of his unfinished, previously unpublished work.

Introduction to the Collection

Charles reich's unfinished work, the individual sector: a book proposal, the rise of lawless power: a book proposal, constituting security and fairness: reflecting on charles reich’s imagination and impact.

Charles Reich, The New Property , 73 Yale L.J. 733 (1964).

Id. at 751-55 (outlining basic procedural rights and entitlements).

Id . at 760-64 (outlining basic constitutional issues raised by entitlements, including the right against self-incrimination, the right against unreasonable searches, and First Amendment rights).

Id . at 734, 786-87.

397 U.S. 254, 263 n.8 (1970) (“It may be realistic today to regard welfare entitlements as more like ‘property’ than a ‘gratuity.’” (first citing Charles A. Reich, Individual Rights and Social Welfare: The Emerging Legal Issues , 74 Yale L.J. 1245, 1255 (1965); and then citing Reich, supra note 1 )) .

Reich’s influence has been recognized by recent precedent. See, e.g. , Hillcrest Prop., LLP v. Pasco Cty ., 915 F.3d 1292, 1298 n.8 (11th Cir. 2019) (citing Reich for his definition of new property); George Washington Univ. v. District of Columbia, 318 F.3d 203, 207 (D.C. Cir. 2003 ),  as amended  (Feb. 11, 2003) (outlining use of “new property” inquiry in land-use decisions); Cook v. Principi , 318 F.3d 1334, 1353 (Fed. Cir. 2002) ( Gajarsa , J., dissenting) (citing Reich for the claim that statutory entitlements are new property subject to the Due Process Clause); Hixson ex rel. Hixson Farms v. U.S. Dep’t of Agric., No. 15-CV-02061, 2017 WL 2544637, at *6 (D. Colo. June 13, 2017) (citing Reich to support the claim that a farm subsidy is an entitlement subject to the Due Process Clause); Ames Constr. Co. v. Dole, 727 F. Supp. 502, 504-05 (D. Minn. 1989) (citing Reich to support the claim that a payment due under a government contract is a type of property under the Due Process Clause); Am. Int’l Gaming Ass’n , Inc. v. La. Riverboat Gaming Comm’n, 838 So. 2d 5, 21-22 (La. Ct. App. 2002) (Gonzales, J., concurring) (citing Reich for the claim that “ a license, once issued, albeit a privilege cannot be withdrawn by state action without affording the holders of that license the full procedural protection of due process”). Additionally, Reich’s influence has been reinforced by recent scholarship. See, e.g. , Gregory Ablavsky , The Rise of Federal Title , 106 Calif. L. Rev. 631, 679 (2018) (noting the resemblance between “new property” and “old property” in assessment of federal title); Ronald A. Cass & Jack M. Beermann ,  Throwing Stones at the Mudbank: The Impact of Scholarship on Administrative Law , 45 Admin. L. Rev. 1, 12 (1993) (discussing scholarship related to procedural due-process claims and noting that “[ th ]e apparent effect of Reich’s work in confirming the instinct of Justices forming the Goldberg and Roth majorities (that procedural guarantees should cover claims to government benefits) stands in marked contrast to the apparent disinterest of courts in the body of scholarship telling courts what to do next”); Danielle Keats Citron, Comment, A Poor Mother’s Right to Privacy: A Review, 98 B.U. L. Rev. 1139, 1152-55 (2018) (outlining Reich’s influence on the due-process rights afforded to the indigent); Bethany Y. Li, Now Is the Time!: Challenging Resegregation and Displacement in the Age of Hypergentrification, 85 Fordham L. Rev. 1189, 1215 (2016) (discussing Reich’s analysis of procedural rights with respect to the new property) .

Richard J. Pierce, Jr., The Due Process Counterrevolution of the 1990s? , 96 Colum. L. Rev. 1973, 1974-80 (1996) (outlining a receding commitment to the “due process revolution” initiated by the expansive claims of Reich and their acceptance by the Supreme Court in Goldberg v. Kelly ); Thomas W. Merrill, Jerry L. Mashaw , the Due Process Revolution, and the Limits of Judicial Power , in Administrative Law from the Inside Out: Essays on Themes in the Work of Jerry L. Mashaw 39, 58-59 (Nicholas R. Parrillo ed., 2017) (contending that the threshold interests in life, liberty, and property should be read narrowly as opposed to in broad Reichian fashion).

Welfare (Zipporah Films 1975). Welfare examines the day-to-day life of a welfare office in New York in the 1970s.

Richard Brody, DVD of the Week: Welfare , New Yorker , https://www.newyorker.com /culture/ richard-brody / dvd -of-the-week-welfare [https://perma.cc/UA7F-JF4K].

72  Yale L.J.  1347 (1963).

Reich, supra note 1.

74 Yale L.J. 1245 (1965).

Reich should be situated in a broader movement in the 1950s and 1960s that directed the administrative state from macrolevel perspectives to a microlevel perspective on administrative law. See, e.g. , Bernard Schwartz,  Crucial Areas in Administrative Law , 34  Geo. Wash. L. Rev.  401, 406 (1965) (“Rather, we shall attempt to touch upon three representative areas that are bound to be of crucial concern to the administrative lawyer of the next quarter century. The first of these is that of administrative power over the physical person itself; the second, that of administrative intrusion into physical privacy; and the third, that of administrative largess in the Welfare State.”).

Here, I adopt a definition of spatiality articulated by Nicholas Blomley . See Nicholas Blomley , Law, Property, and the Geography of Violence: The Frontier, the Survey and the Grid , 93 Annals Ass’n Am. Geographers 121, 122-23 (2003) (outlining the socio-legal context of the term space).

Charles A. Reich, Police Questioning of Law Abiding Citizens , 75 Yale L.J. 1161, 1166-67 (1966) (outlining interactions of citizens with police and noting that “[m] ost of these [police] practices have grown up around the automobile”).

Reich, supra note 10 (outlining welfare raids at home).

Charles A. Reich, The Law of the Planned Society , 75 Yale L.J. 1227, 1227-28 (1966) (outlining disputes regarding the planning process associated with highways in which protestors occupied the planned sites of new highways).

Sarah A. Seo , The New Public , 125 Yale L.J. 1616 , 1622 (216).

Joshua Chanin , Police Reform Through an Administrative Lens: Revisiting The Justice Department’s Pattern and Practice Initiative , 37 Administrative Theory and Practice 257-74, 260 (2017) (examining why public administration scholars have ignored the Department of Justice’s pattern and practice orders as an element of administrative police reform).

U .S. Dep’t of Justice Civil Rights Div. , Investigation of the Ferguson Police Department 15-70 (Mar. 4, 2015) (outlining the police and municipal practices that lead to the erosion of community trust).

Sidney Shapiro, Elizabeth Fisher & Wendy Wagner, The Enlightenment of Administrative Law: Looking Inside the Agency for Legitimacy, 47 Wake Forest L. Rev. 463, 467-71 (2012) (outlining models of administrative legitimacy, including the rationalist-instrumental paradigm and the deliberative-constitutional paradigm).

For an example of this approach, see Sameena Mulla, Sexual Violence, Law, and Qualities of Affiliation , in Wording the Word 172, 175 (Roma Chatterji ed., 2014) (using an anthropological approach to assess a sexual-assault victim’s encounter with the state).

Kali Murray & Esther van Zimmeren , Dynamic P atent G overnance in Europe and the United States: The Myriad E xample , 19 Card. Int. & Comp. L. Rev. 287 , 295 (2011) (“We observe that the idea of network governance is emerging within the context of patent law, and extend this model in two additional ways. First, we claim that within its formal dimensions, the patent system should be analyzed as a whole, focusing on the roles played by various actors, rather than the individual institutional actors themselves. This focus on roles, rather than individual actors, also greatly facilitates comparison of governance systems between different jurisdictions.”); Robert B. Ahdieh ,  From Federalism to Intersystemic Governance: The Changing Nature of Modern Jurisdiction, 57 Emory L.J. 1, 4 (2007) (“O ur collective conceptions of jurisdiction would seem to be in significant flux, with increasing attention to complex patterns of overlap and engagement, not only among courts, but also among social, political, and economic actors more generally.”).

Reich, supra note 12, at 1254-56.

Id . at 1254.

See, e.g. , Stewart v. Azar, 313 F. Supp. 3d 237, 269 (D.D.C. 2018) (describing how Section 1396(a) of the Affordable Care Act placed “ all individuals whose income fell below prescribed levels” into Medicaid’s mandatory population. In so doing, the Affordable Care Act “placed this group on equal footing with other ‘vulnerable’ populations, requiring that states afford them ‘full benefits.’”). Although the litigation is ongoing, it appears that a key element of the Affordable Care Act is the fact that the institutional design of its statutory scheme affords equal protection in the treatment of an expanded Medicaid population.

Virginia Eubanks, Digital Dead End: Fighting For Social Justice in the Information Age 82-83 (2011); see also Khiara M. Bridges , The Poverty of Privacy Rights 133-79 (2017) (outlining the erosion of informational privacy for working women receiving public assistance); John Gilliom , Overseers of the Poor 115-36 (2001) (outlining surveillance tools employed by the administrative state).

See, e.g. , Gillian E. Metzger, Administrative Constitutionalism , 91 Tex. L. Rev. 1897, 1898-900 (2013) (discussing how agencies conduct constitutional analyses); Karen M. Tani , Administrative Equal Protection: Federalism, the Fourteenth Amendment, and the Rights of the Poor , 100 Cornell L. Rev. 825 (2015) (outlining the efforts of the Federal Social Security Board to promulgate a theory of administrative equal protection in the institutional design of welfare assistance).

See, e.g. , Gillian E. Metzger, Abortion, Equality, and Administrative Regulation , 56 Emory L.J. 865, 888-89 (2007) (examining unsuccessful efforts by abortion advocates to challenge federal and state administrative actions on abortion). This scholarship, however, does not fully incorporate Reich’s sensitivity toward individuals before the state.

Reich, supra note 10, at 1347.

Reich, supra note 12, at 1246.

See also Ayesha K. Hardison , Writing Through Jane Crow: Race and Gender and Politics in African American Literature 3 (2014); Pauli Murray & Mary O. Eastwood,  Jane Crow and the Law: Sex Discrimination and Title VII , 34  Geo. Wash. L. Rev.  232, 239 (1965) (comparing the functional attributes of sex and race) ; Serena Mayeri ,  The Strange Career of Jane Crow: Sex Segregation and the Transformation of Anti-Discrimination Discourse , 18 Yale J.L. & Human. 187, 188 (2006) (“E xamining the theory and practice of Jane Crow helps to elucidate the cultural ramifications of, and interactions among, racial integration, shifting sexual mores, gender politics, and legal change during this period.”).

See Priscilla A. Ocen ,  The New Racially Restrictive Covenant: Race, Welfare, and the Policing of Black Women in Subsidized Housing , 59  UCLA L. Rev. 1540, 1559-64 (2012) (outlining the treatment of black women in the modern welfare state).

Id. at 1548.

Goldberg v. Kelly, 397 U.S. 254, 268-69 (1970).

Martha Davis , Brutal Need: Lawyers and the Welfare Rights Movement , 1960-1973, at 82-86 (1993) (outlining Reich’s relationship with welfare-rights lawyers); see also The Law of the Poor (Jacobus TenBroek ed., 1966) (providing an interdisciplinary review of the law of the poor).

Atiba R. Ellis , Race, Class, and Structural Discrimination: On Vulnerability Within the Political Process , 28 J. C.R. & Econ. Dev. 33, 34 (2015).

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Boyle’s Law – Definition, Formula, Example

Boyle’s law or Mariotte’s law states that pressure of an ideal gas is inversely proportional to volume under conditions of constant mass and temperature. When the gas volume increases, pressure decreases. When the volume decreases, pressure increases. Boyle’s law takes its name from chemist and physicist Robert Boyle , who published the law in 1862.

Boyle’s law states that the absolute pressure of an ideal gas is inversely proportional to its volume under conditions of constant mass and temperature.

Boyle’s Law Formula

There are three common formulas for Boyle’s law:

P ∝ 1/V PV = k P 1 V 1 = P 2 V 2

P is absolute pressure, V is volume, and k is a constant.

Graphing Boyle’s Law

The graph of volume versus pressure has a characteristic downward curved shape that shows the inverse relationship between pressure and volume. Boyle used the graph of experimental data to establish the relationship between the two variables.

Richard Towneley and Henry Power described the relationship between the pressure and volume of a gas in the 17th century. Robert Boyle experimentally confirmed their results using a device constructed by his assistant, Robert Hooke. The apparatus consisted of a closed J-shaped tube. Boyle poured mercury into the tube, decreasing the air volume and increasing its pressure. He used different amounts of mercury, recording air pressure and volume measurements, and graphed the data. Boyle published his results in 1662. Sometimes the gas law is called the Boyle-Mariotte law or Mariotte’s law because French physicist Edme Mariotte independently discovered the law in 1670.

Examples of Boyle’s Law in Everyday Life

There are examples of Boyle’s law in everyday life:

• The bends : A diver ascends to the water surface slowly to avoid the bends. As a diver rises to the surface, the pressure from the water decreases, which increases the volume of gases in the blood and joints. Ascending too quickly allows these gases to form bubbles, blocking blood flow and damaging joints and even teeth.
• Air bubbles : Similarly, air bubbles expand as they rise up a column of water. If you have a tall glass, you can watch bubble expand in volume as pressure decreases. One theory about why ships disappear in the Bermuda Triangle relates to Boyle’s law. Gases released from the seafloor rise and expand so much that they essentially become a gigantic bubble by the time they reach the surface. Small boats fall into the bubbles and are engulfed by the sea.
• Deep-sea fish : Deep-sea fish die if you bring them up to the surface. As outside pressure drops, the volume of gas within their swim bladder increases. Essentially, the fish blow up or pop.
• Syringe : Depressing the plunger on a sealed syringe decreases the air volume inside it and increases its pressure. Similarly, if you have a syringe containing a small amount of water and pull back on the plunger, the volume of air increases, but it’s pressure decreases. The pressure drop is enough to boil the water within the syringe at room temperature.
• Breathing: The diaphragm expands the volume of the lungs, causing a pressure drop that allows outside air to rush into the lungs (inhalation). Relaxing the diaphragm reduces the volume of the lungs, increasing the gas pressure within them. Exhaling occurs naturally to equalize pressure.

Boyle’s Law Example Problem

For example, calculate the final volume of a balloon if it has a volume of 2.0 L and pressure of 2 atmospheres and the pressure is reduced to 1 atmosphere. Assume temperature remains constant.

P 1 V 1 = P 2 V 2 (2 atm)(2.0 L) = (1 atm)V 2 V 2 = (2 atm)(2.0 L)/(1 atm) V 2 = 4.0 L

It’s a good idea to check your work to make sure the answer makes sense. In this example, the balloon pressure decreased by a factor of two (halved). The volume increased and doubled. This is what you expect from an inverse proportion relationship.

Most of the time, homework and test questions require reasoning rather than math. For example, if volume increases by a factor of 10, what happens to pressure? You know increasing volume decreases pressure by the same amount. Pressure decreases by a factor of 10.

See another Boyle’s law example problem .

• Fullick, P. (1994).  Physics . Heinemann. ISBN 978-0-435-57078-1.
• Holton, Gerald James (2001). Physics, The Human Adventure: From Copernicus to Einstein and Beyond . Rutgers University Press. ISBN 978-0-8135-2908-0.
• Tortora, Gerald J.; Dickinson, Bryan (2006). ‘Pulmonary Ventilation’ in Principles of Anatomy and Physiology (11th ed.). Hoboken: John Wiley & Sons, Inc. pp. 863–867.
• Walsh, C.; Stride, E.; Cheema, U.; Ovenden, N. (2017). “A combined three-dimensional in vitro–in silico approach to modelling bubble dynamics in decompression sickness.” Journal of the Royal Society Interface . 14(137). doi: 10.1098/rsif.2017.0653
• Webster, Charles (1965). “The discovery of Boyle’s law, and the concept of the elasticity of air in seventeenth century”. Archive for the History of Exact Sciences . 2(6) : 441–502.

Related Posts

Charles Law Lab Report Essay Example

• Pages: 4 (852 words)
• Published: April 28, 2017
• Type: Laboratory Work

The volume of the air sample at the high temperature, (Vn),decreases when the sample is cooled to the low temperature and becomesV1. All of these measurements are made directly. The experimental data is then used to verify Charles'law by two methods: 1. The experimental volume (V""o) measured at the low temperature is compared to the V1 predicted by Charles' law where Yy(t oretic (vH,[ he at)= + ) 165 2. The V/T ratios for the air sample measured at both the high and the low temperatures are compared. Charles'law predicts that these ratios will be equal. V"_V" TH TL

Pressure Considerations

The relationship between temperature and volume defined by Charles' law is valid only if the pressure is the same when the volume is measured at each temperature. That is not the case in this experiment.

• The volume, Vs, of air at the higher temperature, Ts, is measured at atmospheric pressure' P"t* in a dry Erlenmeyer flask. The air is assumed to be dry and the pres. nr" is obtained from a barometer.
• The experimental air volume, (V"*p) at the lower temperature, Tp, is measured. over water. This volume is saturated with water vapor that contributes to the total pressure in the flask.

Therefore, the experimental volume must be corrected to the volume of dry anrat atmospheric pressure. This is done using Boyle's law as follows: a. The partial pressure of the dry air, Poo, is calculated by subtracting the vapor pressure of water from atmospheric pressure: P. r--PffrO=POA b. The volume that this dry air would occupy at Pur,''is then calculated using the Boyle's law equation: = (%,. oXp*) (voo)(%,_) (%,. oXp*). =Sff

(voo) PROCEDURE Wear protective glasses. NOTE: It is essential that the Erlenmeyer flask and rubber stopper assemblvbe as drv as possiblein order to obtain reproducibleresults.

Dry a L25 mL Erlenmeyer flask by gently heating the entire outer surface with a burner flame. Care must be used in heating to avoid breaking the flask. If the flask is wet, first wipe the inner and outer surfaces with a towel to remove nearly all the water. Then, holding the flask with a test tube holder, gently heat the entire flask. Avoid placing the flask directly in the flame. Allow to cool. While the flask is cooling select a l-hole rubber stopper to fit the flask and insert a b cm piece of glass tubing into the stopper so that the end of the tubing is flush with the bottom of 66 the stopper. Attach a 3 cm piece of rubbertubingto the glass tubing (see Figure 19. 1-). Insert (wax pencil) the distance that it is inserted. Clamp the the stopper into the flask and mark flask so that it is submerged as far as possible in water contained in a 400 mL beaker (without the flask touching the bottom of the beaker) (see Figure I9. 2). Heat the water to boiling. Keep the flask in the gently boiling water for at least 8 minutes to allow the air in the flask to attain the temperature of the boiling water. Add water as needed to maintain the water level in the beaker.

Read and record the temperature of the boiling water. While the flask is still in the boiling water, seal it by clamping the rubber tubing tightly

with a screw clamp. Remove the flask from the hot water and submerge it in a pan of cold water, keeping the top down at all times to avoid losing air. Remove the screw clamp, letting the cold water flow into the flask. Keep the flask totally submerged for about 6 minutes to allow the flask and contents to attain the temperature of the water. Read and record the temperature of the water in the pan. Figure 19. Rubber stopper assembly Figure 19. 2 Heating the flask (and air) in boiling water t67 In order to equalize the pressure inside the flask with that of the atmosphere, bring the water level in the flask to the same level as the water in the pan by raising or lowering the flask (see Figure 19. 3). With the water levels equal, pinch the rubber tubing to close the flask. Remove the flask from the water and set it down on the laboratory bench. Using a graduated cylinder carefully measure and record the volume of liquid in the flask. Repeat the entire experiment.

Use the same flask and flame dry again; make sure that the rubber stopper assembly is thoroughly dried inside and outside. After the second trial fill the flask to the brim with water and insert the stopper assembly to the mark, letting the glass and rubber frll to the top and overflow. Measure the volume of water in the flask. Since this volume is the total volume of the flask, record it as the volume of air at the higher temperature. Because the same flask is used in both trials. it is necessarv to make

this measurement onlv once. Figure 19. 3 Equalizing the pressure in the flask.

The water level inside the flask is adjusted to the level of the water in the pan by raising or lowering the flask.

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