Differentiate between specific heat capacities at constant volume and constant pressure?

Specific heat capacity at constant volume (Cv) is the amount of heat required to raise the temperature of a unit mass of a substance by 1 degree Celsius at constant volume, while specific heat capacity at constant pressure (Cp) is the amount of heat required to raise the temperature of a unit mass of a substance by 1 degree Celsius at constant pressure.

The main difference between the two is that at constant volume, the substance does not expand or contract, so all the heat added goes into increasing the temperature of the substance. On the other hand, at constant pressure, the substance can expand or contract, so some of the heat added goes into doing work on the surroundings, in addition to increasing the temperature of the substance.

Mathematically, the relationship between Cp and Cv is given by the equation Cp = Cv + R, where R is the gas constant. This relationship holds true for ideal gases.