An experiment is performed to measure the molar heat capacity of a gas at constant pressure using Regnault's method. The gas is initially contained in a cubical reservoir of size ` 40 cm xx 40 cm xx 40 cm xx at 600 kPa at 27^0C`. A part of the gas is brought out, heated to 100^0C and is passed through a calorimeter at constant pressure. The water equivalent of the calorimeter and its contents increases from `20^0C to 30^0C` during the experiment and the pressure in the reservoir decresases to `525 kPa`. Specific heat capacity of water =`4200 J kg^(-1) K^(1). Calculate the molar heat capacity Cp from these data.

Explanation

We have `pV = nRT` or, n = pV/ RT. The amount of
the gas in the reservoir is n^(1) = p^(1)V/ RT before the gas is taken
out and n^(2) = p_2V / RT after the gas is taken out is
`Delta n = n_1 - n_2 = (p_1- P_2) V /RT
(600 -525) xx 10^(3) N m ^(-2) xx (40 xx 10 ^(-2) m^(-3) / (8.3 J K^(-1) mol^(-1) xx (300 K)
(300 K) = 1.925 mol`.