Consider one mole of perfect gas in a cylinder of unit cross section with a piston attached (Fig.). A spring (spring constant k) is attached (unstretched length L) to the piston and to the bottom of the cylinder. Initially the spring is unstretched and the gas is in equilibrium. A certain amount of heat Q is supplied to the gas causing an increase of volume from V₀ to V₁. (a) What is the initial pressure of the system? (b) What is the final pressure of the system? (c) Using the first law of thermodynamics, write down a relation between Q, Pa, V, V₀ and k. Which of the following gives the correct final result?

Question

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). Evaluating the given data/statements gives P₁=Pₐ; P₂=Pₐ+k(V-V₀); Q=Pₐ(V-V₀)+½k(V-V₀)²+Cᵥ(T-T₀). Therefore the correct answer is A.