Question

For an ideal gas , the molar specific heat capacities at constant pressure and volume satisfy the relation Cp - Cv = R where R is the universal gas constant.​

Answer 1

Specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of a unit mass of substance through 1ºC.

While defining the specific heat capacity, it was assumed that whole of the heat supplied to the substance is used in raising its temperature and in another way. This assumption holds good in the case of solids and liquids since expansion, in them due to 1ºC rise of temperature is negligible. Gases expand quite appreciably due to a rise in temperature. Therefore, heat required by the gas to do external work cannot be neglected.

A gas can be heated in two ways. Accordingly, there are two specific heat capacities in case of a gas.