Question

Three samples of the same gas A, B and C $(\gamma =\frac{3}{2})$ 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 pressure is:

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

Answer 1

The correct option is B $2\sqrt{2}:1:2$

For isobaric process, pressure will remain same, $P_B=P$

For isothermal process, $P_1{V}_1=P_2{V}_2⟹P_C\times V=P\times 2V$

So, $P_C=2P$

For adiabatic process, $P{V}^{\gamma }⟹P_A{V}^{1.5}=P(2V{)}^{1.5}$

$P_A=2\sqrt{2}P$

Therefore, $P_A:P_B:P_C=2\sqrt{2}:1:2$