Molar Heat Capacity of different phases of matter

[Eden K 1B]

Why do you have to specify pressure or volume for a gas but not for a solid or liquid when calculating the molar heat capacity? For example, we have the terms Cv and Cp for gases but not for solids and liquids.

[Gregory_Kislik_2C]

When heating a solid or liquid, the change in volume is negligible. For example, when I heat 100 ml of liquid water from 10 degrees Celsius to 50 degrees Celsius, its volume will still be very close to 100 ml (in reality, there is some small change - I believe that liquid water is most dense at 4 degrees Celsius, so the same number of moles would occupy a smaller volume at that point, but even this difference is negligible for our purposes). Additionally, liquids do not exert a significant pressure on their containers, so there is no need to have a specific molar heat capacity for that reason either. Solids similarly do not exert a pressure on the walls of their container, nor do their volumes change much with heating or cooling.

Gases are different however. At a constant volume, all of the work which is done on a gas will go into the heat/energy of the molecules, i.e. it will increase their enthalpy (since enthalpy is the change in heat at constant pressure), so that requires its own specific heat capacity. Beyond this, at constant pressure, heated gases will expand in volume and as a result do expansion work, which will change their internal energy (delta U = q + w, where w is -PdeltaV, since the pressure is constant). As a result, this needs to be factored into the constant pressure heat capacity, as some of the energy which is put into the system will be used in the process of expanding the gas.

I hope this helps and please let me know if there are any errors.