Question

Three samples of the same gas A, B and $C(\gamma =\frac{3}{2})$ 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 $P_C$, then $P_A(V{)}^{\frac{3}{2}}=(2V{)}^{\frac{3}{2}}P,P_B=P$ and $P_C\left(V\right)=P\left(2V\right)$

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