Two thermally insulated vessels A and B contain an ideal monoatomic gas and are connected by a small tube with a valve. Initially A contains 2 L of gas at 300 K and 2×10⁵ Pa, while B contains 4 L at 350 K and 4×10⁵ Pa. The valve is opened and equilibrium is reached. Find the final pressure and temperature. Take R=25/3 J mol⁻¹ K⁻¹.
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Question

Two thermally insulated vessels A and B contain an ideal monoatomic gas and are connected by a small tube with a valve. Initially A contains 2 L of gas at 300 K and 2×10⁵ Pa, while B contains 4 L at 350 K and 4×10⁵ Pa. The valve is opened and equilibrium is reached. Find the final pressure and temperature. Take R=25/3 J mol⁻¹ K⁻¹.

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G1 Physics · Accepted Answer

Use PV=nRT, U=(f/2)nRT, γ=1+2/f and vᵣₘₛ=√(3RT/M). At the same temperature, average translational kinetic energy depends only on T. Evaluating the given data/statements gives P=(10/3)×10⁵ Pa; T=10500/31 K≈338.7 K. Therefore the correct answer is A.