Question

One mole each of monatomic, diatomic and triatomic ideal gases (kept in three different containers) whose initial volume and pressure are same, each is compressed till their pressure becomes twice the initial pressure. Then which of the following statements is/are incorrect?

• A. If the compression is isothermal then their final volumes will be same
• B. If the compression is adiabatic, then final volume will be different
• C. If the compression is adiabatic, then triatomic gas will have maximum final volume
• D. If the compression is adiabatic, then monoatomic gas will have maximum final volume

Answer 1

Answer: (A), (D)

The correct options are
A If the compression is isothermal then their final volumes will be same
D If the compression is adiabatic, then monoatomic gas will have maximum final volume

If the process is isothermal, then the volume has to change in order to compensate for the change in pressure.
If the compression is adiabatic, then the triatomic gas will have the maximum value because of the value of $\gamma$
Since, the adiabatic gas law will be followed, $P{V}^{\gamma }$ = C
$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }\Rightarrow P_0{V}_0^{\gamma }=2P_0{V}_2^{\gamma }$
$V_2={\left(\frac{1}{2}\right)}^{\gamma }{V}_0\Rightarrow V_2=\frac{V_0}{2^{\gamma }}$
Monoatomic gas $\gamma$ is min $V_2$ is max.