Question

For an ideal gas, the specific heat at constant pressure $C_p$ is greater than the specific heat at constant volume $C_v$. This is because

• A. There is a finite work done by the gas on its environment when its temperature is increased while the pressure remains constant
• B. There is a finite work done by the gas on its environment when its pressure is increased while the volume remains constant
• C. There is a finite work done by the gas on its environment when its pressure is increased while the temperature remains constant
• D. The pressure of the gas remains constant when its temperature remains constant
• E. The internal energy of the gas at constant pressure is more than at constant volume

Hint:

Extra heat at constant pressure goes into doing work, hence $C_p > C_v$.

Answer 1

The Correct Option is A

Concept:
At constant pressure, gas expands and does work.

Step 1: Constant volume case.
No work is done: \[ W = 0 \]

Step 2: Constant pressure case.
Gas expands and does work: \[ W = P\Delta V \]

Step 3: Conclusion.
More heat required at constant pressure: \[ C_p > C_v \]