Specific Heat Capacity of Gas

Gases behave differently from solids and liquids when heated: even a small temperature change can be accompanied by a considerable change in BOTH volume and pressure. If a gas is heated at constant pressure, it is free to expand, and some of the supplied heat goes into doing work against the surroundings during that expansion (rather than only raising the gas's internal energy/temperature) -- so MORE heat is required for the same temperature rise than if the volume were held fixed. Consequently, the specific heat at constant pressure $S_p$ is always greater than the specific heat at constant volume $S_v$, and gases must be described using two distinct principal specific heats:

$S_v$ (at constant volume): the heat absorbed or released per unit mass of gas for a 1 K (1 °C) rise or fall of temperature, with volume held fixed.

$S_p$ (at constant pressure): the same, but with pressure held fixed instead.

The corresponding MOLAR specific heats, $C_v$ and $C_p$, are defined identically but per mole of gas rather than per unit mass, and are related to the principal specific heats by the molecular weight $M$ of the gas:

$C_p = M \times S_p, \qquad C_v = M \times S_v$ …