Question

Three samples of the same gas $A,B$ and $C(\gamma =3/2)$ have equal volume initially. Now, the volume of each sample is doubled. For $A$ , the process is adiabatic; for $B$ , it is isobaric and for $C$ , the process is isothermal. If the final pressure are equal for all the three samples, the ratio of their initial pressures is

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

Answer 1

Answer: (B)

Let $P_A,P_B,P_C$ be the initial pressure of the three samples and $P$ is the final pressure of each.
For $A$ , the process is adiabatic
$\therefore P_A(V{)}^{3/2}=P(2V{)}^{3/2},P_A=P{2}^{3/2}$
For $B$ , the process is isobaric,
$\therefore P_B=P$
For $C$ , the process is isothermal,
$\therefore P_C(V)=P(2V),P_C=2P$
Hence $P_A:P_B:P_C=2^{3/2}:1:2=2\sqrt{2}:1:2$