Question

Three samples of the same gas $A,B$ and $C$ each of $\gamma =\frac{3}{2}$ have initially equal volume. Now the volume of each sample is doubled. The process is adiabatic for $A$, isobaric for $B$ and isothermal for $C$. If the final pressures are equal for all three samples, the ratio of their initial pressures are

• A. $2\sqrt{2}:2:1$
• B. $2\sqrt{2}:1:2$
• C. $\sqrt{2}:1:2$
• D. $2:1:\sqrt{2}$

Answer 1

The correct option is B $2\sqrt{2}:1:2$

Let the initial pressure of the three samples be $P_A,P_B$ and $P_C$,
Final pressure of all gases be $P$

Process for $A$ is adiabatic
$P_A(V{)}^{\frac{3}{2}}=(2V{)}^{\frac{3}{2}}P$

Process for $B$ is isobaric

$P_B=P$ and

Process $C$ is isothermal
$P_C\left(V\right)=P\left(2V\right)$

$\Rightarrow P_A:P_B:P_C=(2{)}^{\frac{3}{2}}:1:2=2\sqrt{2}:1:2$