MCQ
Three samples of the same gas $A, B$ and $C \left(\gamma=\frac{3}{2}\right)$ 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 the three samples, the ratio of their initial pressures is:
  • A
    $\sqrt{2}: 1: 2$
  • B
    $2: 1: \sqrt{2}$
  • C
    $2 \sqrt{2}: 2: 1$
  • D
    $2 \sqrt{2}: 1: 2$

Answer

D. $2 \sqrt{2}: 1: 2$
Explanation:
Let the initial pressure of the three samples $P _{ A }, P _{ B }$ and $P _{ C }$, then
$\begin{array}{l}
P_{A}(V)^{3 / 2}=(2 V)^{3 / 2} P\left(\because P_{B}=P\right) \\
\text { or } P_{A}=P(2)^{3 / 2} \\
P_{C}(V)=P(2 V) \\
\text { or } P_{C}=2 P \\
\therefore P_{A}: P_{B}: P_{C} \\
=(2)^{3 / 2}: 1: 2=2 \sqrt{2}: 1: 2
\end{array}$

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