Calculate the heat capacity of a gas sample from the following information: the sam- ple comes to equilibrium in a flask at 25°c and 121.3 kpa. a stopcock is opened briefly, allowing the pressure to drop to 101.3 kpa. with the stopcock closed, the flask warms, returning to 25°c, and the pressure is measured as 104.0 kpa. determine cp in j·mol−1·k−1 assuming the gas to be ideal and the expansion of the gas remaining in the flask to be reversible and adiabatic.

Answer : The  value of for reversible and adiabatic expansion is 55.04 J/mol.K

Explanation : Given,

Temperature at equilibrium =

Pressure at equilibrium =

Temperature at adiabatic reversible expansion =

Pressure at adiabatic reversible expansion =

Temperature at constant volume process =

Pressure at constant volume process =

First we have to calculate the temperature at adiabatic reversible expansion.

Gay-Lussac's Law : It is defined as the pressure of the gas is directly proportional to the temperature of the gas at constant volume and number of moles.

or,

Now put all the given values in the above equation, we get:

Now we have to calculate the value of for reversible and adiabatic.

Formula used :

Now put all the given values in the above equation, we get:

Therefore, the value of for reversible and adiabatic expansion is 55.04 J/mol.K