Why gas has two specific heat but solid and liquid has only one?
Answers
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.