Using the Process Condition

• A fixed piston means the gas volume does not change.
• No boundary moves, so no pressure-volume work is done.

• For a fixed amount of ideal gas, internal energy depends only on thermodynamic temperature.
• If the temperature is unchanged, the internal energy is unchanged. If the temperature rises, the internal energy rises.
• Fast compression can raise the temperature because positive work is done on the gas. If little energy leaves by heating, most of that work increases internal energy.

• Compare the same fixed amount of ideal gas with the same starting and final temperatures. The increase in internal energy is the same.
• At constant volume, no volume work is done. All the supplied thermal energy increases internal energy.
• At constant pressure, the gas expands and does work as well. More thermal energy is needed for the same temperature rise.

Therefore the measured specific heat capacity at constant pressure is greater than the value at constant volume (9702/42/F/M/24 Q2(c)).