Question

Three samples of the same gas A , B and C(g = 3/2) have initially equal volume. Now the volume of each sample in doubled. The process is adiabatic for A isobaric for B and isothermal for C. If the final pressures 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 : $\sqrt { 2 }$

Answer 1

Answer: (B)

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

Answer 2

For A, P_A V^g = P (2V)^g

P_A = P₂^g ... (1)

for B, P_B = P ... (2)

for C, P_CV = P (2V) P_C = 2P ... (3)

P_A = 2^gP, P_B = P, P_C = 2P

where 'P' is final pressure, so

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