**Experimental Determination of γ of a Gas**

(a) F. Clement and C. B. Desormes used the principle of adiabatic expansion to determine the value of γ. The gas at a pressure greater than one atmosphere is placed in a large vessel (capacity 30-40 L) fitted %3/4 nth a rubber stopper and water or an oil manometer (Figure).

Fig: Clement and Desorme apparatus

The pressure P_{1} is measured. The stopper is suddenly opened and then closed again. The pressure of the gas momentarily becomes equal to that of the atmosphere and during the expansion, which is virtually adiabatic, the gas is cooled. As it warms up again and attains the temperature of the surrounding, the pressure rises to P_{2}. Let V_{1} be the volume of one mole of gas at pressure P_{1} and V be the volume after adiabatic expansion when the pressure is P. For an ideal gas.

** P_{1}V_{1}^{γ} = PV^{γ}** … … … (1)

The initial and final temperatures are the same, the final pressure is P_{2} and the corresponding volume of one mole of gas is V. It follows by Boyle’s law, that,

** P _{1}V_{1} = P_{2}V_{2}** … … … (2)

From the equation 1 and 2, one can obtain;

(P_{1}/P_{2})^{γ} = P_{1}/P

or, **γ = (log P _{1} – log P) / (log P_{1} – log P_{2})**

The ratio of the specific heats may thus be calculated.