Q. Three samples of the same gas $A,B$ and $C(\gamma = 3/2)$ 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 pressure 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) $2\ :1\ :\ \sqrt{2}$
Explanation
(b) Let the initial pressure of the three samples be $P_{A},\ P_{B}$ and $P_{C}$, then $P_{A}(V)^{3/2} = (2V)^{3/2}P,\ P_{B} = P$ and $P_{C}(V) = P(2V)$
$\Rightarrow P_{A}:P_{B}:PC = (2)^{3/2}:1:2 = 2\sqrt{2}:1:2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.