# Charle’s Law – Gas Law Chemistry Notes

## Charle’s Law:

Jacques Charles, in 1662, gave this law. It relates the volume and absolute temperature of ideal gases at constant pressure and mass. It states

“For a fixed mass of a gas, the volume is directly proportional to absolute temperature at constant pressure.”

V         ∝        T          …………….. (1)

This shows that when absolute temperature increases, volume increases to the same fold and vice versa.

V         =          KcT

Or

V / T   =          Kc        ……………. (2)

Thus law can also be stated as:

“For a fixed mass of a gas, the ratio of volume and the absolute temperature remains constant at constant pressure.”

It means volume changes with change in absolute temperature but the ratio V/T remains the same.

Let the volume of a gas is V1 at absolute temperature T1. Then

V1/T1   =          Kc        ……………… (3)

If pressure changes to P2 then the volume will change to V2 such that the ratio remains the same

V2/T2   =          Kc        ……………… (4)

Comparing equations (3) and (4), we can write

V1         =         V2        ……………… (5)

T1                    T2

## Experimental Verification of Charle’s law:

The law can be verified by using the apparatus as shown in the figure. A glass tube closed at one end is taken in which some mercury is poured. The air present in the tube will be trapped at the close end and mercury will act as a frictionless piston. The tube will be placed in the thermostat.

Such that         T1 < T2 < T3

By increasing the temperature it can be seen that volume increases. Thus the law is verified.

Such that         T1 < T2 < T3

By increasing the temperature it can be seen that volume increases. Thus the law is verified.

Law is further verified by plotting a graph for temperature versus volume it gives a straight line which verifies the law.

J.L Gay Lussac also showed a similar relationship between Celsius temperature and volume. It states

“For each one-degree centigrade rise or fall in temperature, the increase or decrease in volume is 1/273 of the volume of gas at 0oC.”

Let the volume of a gas at 0oC = Vo

This temperature at which the volume of a gas becomes hypothetically zero is called absolute zero (i.e. zero of absolute or Kelvin scale).

It shows that Charle’s law and Gay Lussac’s laws are one and the same.

## Explanation of Charle’s Law on the basis of KMT:

Consider a cylinder fitted with a freely movable piston. Let the cylinder contains ‘n’ number of molecules at temperature ‘T’, volume is ‘V’ and pressure exerted by molecules is ‘P’.

Further, consider that temperature is raised to double. As temperature became double so av. K.E also becomes double and in turn, collisions also become double. Thus piston will be pushed up to double volume so that internal and external pressure again becomes equal. It means when temperature increases twice, the volume also increases twice. i.e.

V         ∝        T

And this is the statement of Charle’s law.