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Why does a gas have different specific heats at constant pressure and constant volume?

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heating In a thermoelectric generating system a heat source—usually fueled by coal, oil, or gas—is used within a boiler to convert water to high-pressure steam. The steam expands and turns the blades of a turbine, which turns the armature of a generator, producing electric power. A condenser converts any remaining steam to water, and a pump returns the water to the boiler.

A gas has different specific heats at constant pressure ( $c_{P}$ ) and constant volume ( $c_{V}$ ) because of the work performed during thermal expansion.21

When a gas is heated at constant volume, no work is performed because the volume does not change ( $d V = 0$ ). Consequently, all the heat added to the system goes directly into increasing its internal energy.2

In contrast, when a gas is heated at constant pressure, the gas expands as its temperature rises. To maintain constant pressure, the gas must perform work against the surrounding atmosphere as it pushes against a boundary (such as a piston). Because some of the added heat is consumed to perform this external work, more heat is required to achieve the same temperature increase compared to the constant-volume process. Therefore, $c_{P}$ is always greater than $c_{V}$ . For an ideal gas, this relationship is expressed as $c_{P} = c_{V} + R$ , where $R$ is the universal gas constant.21