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)

$2\sqrt{2} : 1 : 2$

Answer 2

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 $\therefore P_A (V)^{3/2} = P(2V) ^{3/2} , P_A = P2^{3/2}$ 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 $P_A : P_B : P_C = 2^{3/2} : 1 : 2 = 2 \sqrt {2} : 1 : 2$