Question

Choose the correct statement(s) among the following

• A. The work done in an isochoric process is a function of the temperature only
• B. > for all gases, without exception
• C. The work done by a gas in an isobaric process is responsible for different values of and

Answer 1

Answer: (A), (B), (C)

The correct options are
A

The work done in an isochoric process is a function of the temperature only

B

> for all gases, without exception

C

The work done by a gas in an isobaric process is responsible for different values of and

Let's consider an isobaric process at a constant pressure P, resulting in a temperature change $\Delta T$. According to the first law,

$E_{int}=Q-W$

$\Rightarrow n{C}_v\Delta T=n{C}_p\Delta T-W$

$\Rightarrow W=n(C_p-C_v)\Delta T$.

We know, in an isobaric process, when the volume changes by $\Delta V$, the work done by the gas is $P\Delta V$. But, according to ideal gas equation,

$W=P\Delta V=nR\Delta T$

$\Rightarrow n(C_p-C_v)\Delta T=nR\Delta T$

$\Rightarrow C_p-C_v=R$

$\Rightarrow C_p$ > $C_v$, for all gases.