Question

Why do solids and liquids have only 1 specific heat capacity whereas gases have two.

Answer 1

In general specific heat(C) gives us an idea of the amount of energy(heat) we need to provide to a system in order to bring about a unit rise in the temperature of the system. It's value may vary depending on the process you are providing this energy. Hence we have two values of C namely Cv and Cp . Cv for a gas is the change in internal energy (U) of a system with respect to change in temperature at a fixed volume of the system i.e. Cv =(∂ U/∂ T)v whereas Cp for a gas is the change in the enthalpy (H) of the system with respect to change in temperature at a fixed pressure of the system i.e Cp = (∂ H/∂ T)p. We know that, ΔH = ΔU + PΔV (+ VΔP, ΔP=0 for constant pressure) . So the enthalpy term is greater than the internal energy term because of the PΔV term i.e in case of a constant pressure process more energy is needed, to be provided to the system as compared to that of a constant volume process to achieve the same temperature rise, as some energy is utilized in the expansion work of the system. And the relation that correlates these two is Cp = Cv + R But since liquids and solids can practically assumed to be incompressible, Cp and Cv for them have almost same values and hence only a single value of specific heat is used for them.