Why is the specific heat of a gas greater at constant pressure than at constant volume?

The specific heat of a gas at constant pressure ($c_P$) is always greater than its specific heat at constant volume ($c_V$) because of the work performed during thermal expansion.1

When a gas is heated at constant volume, no thermal expansion occurs, meaning the gas does no work against its surroundings. Consequently, all the heat added to the system goes directly into increasing the gas's internal energy.2

In contrast, when a gas is heated at constant pressure, it expands as its temperature rises. To accommodate this increase in volume, the gas must perform atmospheric work by pushing against the surrounding pressure. Because some of the added heat is consumed to perform this external work, more total heat must be supplied to achieve the same temperature increase compared to the constant-volume process. For an ideal gas, this relationship is expressed by the equation $c_P=c_V+R$, where $R$ represents the gas constant.21