Question

Write Mayer’s formula. The
molar heat capacities of a gas at constant
pressure
and constant volume are 28.8 J mol−1 K−1
and 20.5 J mol−1 K−1 respectively.
Calculate the gas constant.

Answer 1

we derived Mayer's law in thermodynamics. Mayer's formula is Cp - Cv = R. Here Cp is molar specific heat capacity of an ideal gas at constant pressure, Cv is its molar specific heat at constant volume and R is the gas constant.

Answer 2

Let us consider one mole of an ideal gas enclosed in a cylinder fitted with an airtight and frictionless piston. Let P, V and T be the pressure, volume and absolute temperature of the gas respectively.

Let heat energy Q1 be supplied to the gas be supplied at constant volume so that temperature rises to T + DT. The volume is kept constant by placing additional weight on the piston.

Let the corresponding pressure be P + DP.


where Cv is the molar specific heat at constant volume.


Now, the additional weight is removed from the piston. The piston moves upwards through a distance Dx till the pressure is equal to P. Let V + DV be the new volume of the gas. There will be a decrease in the temperature of the gas due to expansion of the gas. Let heat energy Q2 be supplied to the gas till its temperature becomes T + DT.