Two closed vessels of equal volume are connected by a narrow tube. Initially, both contain air at pressure 90 kPa and temperature 400 K. The temperature of one vessel is maintained at 400 K, while the temperature of the other is raised to 500 K. After equilibrium is established, both vessels have the same final pressure. What is this pressure?
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Question

Two closed vessels of equal volume are connected by a narrow tube. Initially, both contain air at pressure 90 kPa and temperature 400 K. The temperature of one vessel is maintained at 400 K, while the temperature of the other is raised to 500 K. After equilibrium is established, both vessels have the same final pressure. What is this pressure?

Options

G1 Physics · Accepted Answer

Let the volume of each vessel be V and the final common pressure be P. Initially, the total number of moles is n(initial) = 90V ÷ (R×400) + 90V ÷ (R×400) = 180V ÷ (400R). Finally, n(final) = PV ÷ (R×400) + PV ÷ (R×500). Conservation of moles gives 180 ÷ 400 = P(1 ÷ 400 + 1 ÷ 500). Now, 1 ÷ 400 + 1 ÷ 500 = 9 ÷ 2000. Therefore, 0.45 = P×0.0045, P = 100 kPa. Correct option: A.