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# Charle's Law

Charles law states that the volume of an ideal gas is directly proportional to the absolute temperature at constant pressure. The law also states that the Kelvin temperature and the volume will be in direct proportion when the pressure exerted on a sample of a dry gas is held constant.

This law was formulated in the year 1780 by French physicist Jacques Charles. This law was described extensively in his unpublished work.

## What Is Charles Law?

Charles’ law, also sometimes referred to as the law of volumes, gives a detailed account of how gas expands when the temperature is increased. Conversely, when there is a decrease in temperature, it will lead to a decrease in volume.

When we compare a substance under two different conditions, from the above statement, we can write this in the following manner:

V2/V1=T2/T1

OR

V1T2=V2T1

This above equation depicts that as absolute temperature increases, the volume of the gas also goes up in proportion.

In other words, Charle’s law is a special case of the ideal gas law. The law is applicable to the ideal gases that are held at constant pressure, but the temperature and volume keep changing.

## Charles Law Everyday Examples

Here are some examples by which you can understand Charle’s law very easily.

In winter, as the temperature decreases, when you take a basketball outside on the ground, it shrinks. This is the only reason why it is important to check the pressure in the car tyres when you go outside during cold days. This is also the case with any inflated object and explains why it’s a good idea to check the pressure in your car tyres when the temperature drops.

If you overfill a tube that is placed in a pool on a hot day, it can swell up in the sun and burst. Similarly, as the turkey cooks, the gas inside the thermometer expands until it can “pop” the plunger. Pop-up turkey thermometers work based on Charles’ law. Another common application can be seen in the working of a car engine.

## Charles Law Formula

Charle’s Law formula is written as,

VI /TI = VF /TF

Where VI = Initial volume

VF = Final volume

TI = Initial absolute temperature

TF = Final absolute temperature

Here, we should remember that the temperatures are absolute temperatures that are measured in Kelvin, not in ⁰F or ⁰C.

## Derivation of Charles Law

As we are aware of the fact that, at constant pressure, the volume of the fixed amount of the dry gas is directly proportional to absolute temperature, according to Charle’s law. We can represent the statement in the following manner:

V∝T

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

V/T = constant = k

In this, the value of k depends on the pressure of the gas, the amount of the gas and also the unit of the volume.

V*T = k——-(1)

Let us consider V1 and T1 to be the initial volume and the temperature, respectively, of an ideal gas.

Then, we can write equation (1) as

V1/T1=k——-(2)

After it lets change the temperature of the gas to T2. Alternatively, if its volume changes to V2, then we can write,

V2/T2=k——–(3)

Equating the above equations, that is, equations 2 and 3, we get

V1/T1=V2/T2

OR

V1T2=V2T1

You may be unaware of the fact that, on heating up a fixed amount of gas, that is, by increasing the temperature, the volume also increases. Similarly, by lowering the temperature, the volume of the gas decreases. And at 0-degree centigrade, the volume of the gas also increases by 1/273 of its original volume for a unit-degree increase in temperature.

It is important to know, as already discussed above, that the unit of temperature must be in Kelvin, not in Celcius or Fahrenheit, to solve the problems related to Charle’s law. The temperature in Kelvin is also known as the absolute temperature scale. To convert the temperature in Celcius to Kelvin, you need to add 273 to the temperature in the Celsius scale.

According to Charles’ law, which states that the volume (V) of the gas is directly proportional to its temperature (T), that must be in Kelvin.

When the temperature changes one unit of the Kelvin scale, it equals to a change in one Celsius degree. Always remember that 0 on the Kelvin scale means -273 or “Absolute Zero”.

The density of the gas is inversely proportional to the temperature in the Kelvin when it is at a constant mass and pressure.

## Graphical Representation of Charles Law

ISOBAR – The graph between V and T at constant pressure is known as isobar or isoplestics, and it always gives a straight line. A plot of V versus T (°C) at constant pressure is a straight line at – 273.15°C. -273.15 – degree Celcius is the lowest possible temperature. ## Charles Law Application in Real Life

This law has a wide application in daily life. Some are explained below.

• In cold weather or in a cold environment, helium balloons shrink.
• In winter, when the weather is cool, the capacity of the human lung decreases. This makes it more difficult for the athletes to perform on a freezing winter day, and it also makes it difficult for people to go jogging.

## Charles Law Solved Problems

1. A gas occupies a volume of 400cm3 at 0-degree Celcius and 780mm of Hg. How many litres of volume will the gas occupy at 80-degree Celcius and 780 mm Hg?

Solution:

According to the question, V1 = 400 cm3

T1 = o degree Celcius = 0+273 = 273 K

T2 = 80 degree Celcius = 80+273 = 353 K

You need to find the V2.

Here, only the temperature is changing, the pressure remains constant

Using Charle’s law, V1/T1 = V2/T2

Putting the above values in Charle’s law, we get,

400/273 = V2/353

V2 = 400*353/273

V2 = 517.21CM3

Since 1 cubic centimetres = 0.001 litres,

517.21 cubic centimetres = 517.21*10^-3=0.517 litres.

2. A sample of gas has an initial volume of 30.8 L and an initial temperature of -67 degree Celcius. What will be the temperature of the gas if the volume is 21.0 L?

According to the question,

V1 = 30.8 L

T1 =-67 degree celsius = 206 K

T2 = ?

V2 = 21.0L

According to Charle’s law,

V1/T1 = V2/T2

30.8/67 = 21/T2

T2 = 21*67/30.8

= 46.9⁰C

If V1 is the 3.60 L, T1 = 255 K, T2 = 102 K, then find the value of V2.

According to the question V2 =?

As we are aware of Charle’s law,

V1/T1 = V2/T2

3.60/255 = V2/102

V2 = 1.44L

3. A gas occupies 221cm3 at a temperature of 0 C and pressure of 760 mm Hg. What will be the volume at 100 °C?

It is very clear that the pressure is constant, and the mass of the gas doesn’t change, so we can apply Charle’s law here.

The temperature in the question is given in Celcius, so as per the rule of Charle’s law, it must be converted to the absolute temperature, that is, Kelvin, to apply the formula:

V1 = 221cm3; T1 = 273(0+273); T2 = 373 K(100+273)

Now, these given values can be put in the formula to get the final volume.

VI /TI = VF /TF

221/273 = VF/373

By rearranging the above equation, we will get the final volume

VF = (221)*(373)/273 K

VF = 302 cm3

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