Question

$C_p$ is always greater than $C_v$ for a gas. Which of the following statements provides, partly or wholly, the reason for this?

• A. No work is done by a gas at constant volume.
• B. When a gas absorbs heat at constant pressure, its volume must change.
• C. For the same change in temperature, the internal energy of a gas changes by a smaller amount at constant volume than at constant pressure.
• D. The internal energy of an ideal gas is function only of its temperature.

Answer 1

Answer: (A), (B)

No work is done by a gas at constant volume.
When a gas absorbs heat at constant pressure, its volume must change.

$n{C}_{p}dT=H=n{C}_{v}dT+Workdone$

When volume is kept constant, $W=0$.

Then $H=n{C}_{v}dT$

Since $W>0$, $C_p>C_v$