Q.Express the change in internal energy in terms of molar specific heat capacity.

Unlike solids and liquids, which have essentially one specific heat capacity, gases have two distinct specific heat capacities, because heating a gas can be done either at constant pressure or at constant volume, and these require different amounts of heat. Specific heat capacity at constant volume ($s_v$): the heat needed to raise 1 kg of gas by 1 K while its volume is held fixed; since the gas cannot expand, no work is done, and all the supplied heat goes into raising the internal energy alone. Specific heat capacity at constant pressure ($s_p$): the heat needed to raise 1 kg of gas by 1 K while its pressure is held fixed; here the gas is free to expand as it is heated, so part of the supplied heat does external work (pushing back the surroundings) and only the remainder raises the internal energy. Because constant-pressure heating mus …