Two vessels contain the same ideal gas. The larger vessel has twice the volume of the smaller one and contains gas at 8 kPa and 1000 K. The smaller vessel contains gas at 7 kPa and 500 K. The vessels are connected and both are maintained at 600 K. The final common pressure is:
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Question

Two vessels contain the same ideal gas. The larger vessel has twice the volume of the smaller one and contains gas at 8 kPa and 1000 K. The smaller vessel contains gas at 7 kPa and 500 K. The vessels are connected and both are maintained at 600 K. The final common pressure is:

Options

G1 Physics · Accepted Answer

Let the smaller vessel have volume V; the larger vessel then has volume 2V. Initial number of moles: n₁ = P₁(2V)/(RT₁) = (8×2V)/(R×1000), n₂ = P₂V/(RT₂) = (7V)/(R×500). Total moles are conserved. At the final state, total volume is 3V and temperature is 600 K: P f ( 3 V ) / ( R × 600 ) P_f(3V)/(R×600) P f ​ ( 3 V ) / ( R × 600 ) = 16V/(1000R) + 7V/(500R). The right side is (0.016+0.014)V/R = 0.030V/R. Thus, P f × 3 / 600 P_f×3/600 P f ​ × 3/600 = 0.030 ⇒ P f P_f P f ​ = 6 kPa. Correct option: D.