Question

Show that C_P - C_V = R Where [C_P = specific heat at constant pressure ; C_V = specific heat at constant volume and R = Universal Gas constant] for an ideal gas? 

Answer 1

Now, Let first heat the gas at constant volume and temperature increases by

∆T,So, ∆Q = C_v∆T →1) 

Since volume remains the same, hence no work is heating the gas then according to law of conservation of energy, the entire heat supplied goes into raising the internal energy and hence the temperature of the gas.

Now, CV ∆T = ∆U

∆U = increase in the internal energy of the gas Let heat the gas at constant pressure and if the temperature of the gas increases by ∆T but here external work is done to expand the gas hence