An amount n moles of a monatomic gas at initial temperature T₀ is enclosed in a cylinder with a light piston. The surroundings are at Tₛ>T₀ and atmospheric pressure Pₐ. Heat is conducted through the base of area A, thickness x and conductivity K. Assuming all changes are slow, find the piston displacement after time t. Which option is correct?
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Question

An amount n moles of a monatomic gas at initial temperature T₀ is enclosed in a cylinder with a light piston. The surroundings are at Tₛ>T₀ and atmospheric pressure Pₐ. Heat is conducted through the base of area A, thickness x and conductivity K. Assuming all changes are slow, find the piston displacement after time t. Which option is correct?

Options

G1 Physics · Accepted Answer

Use the first law Q=ΔU+W (W by the gas), ΔU=nCᵥΔT for an ideal gas, and the appropriate process relation. For Carnot devices, let T₁ be the cold-reservoir temperature and T₂ be the hot-reservoir temperature; η=1−T₁/T₂ and COP=T₁/(T₂−T₁). At constant external pressure, piston displacement is proportional to temperature rise. Solving the first-order heating equation for slow conduction through the base gives the expression in option A.