An ideal gas at NTP is enclosed in a adiabatic vertical cylinder having area of cross section A = 27cm², between two light movable pistons as shown in the figure. Spring with force constant k = 3700 N/m is in a relaxed state initially. Now the lower piston is moved upwards a height h/2, h being the initial length of gas column. It is observed that the upper piston moves up by a distance h/16. Find h taking γ for the gas to be 1.5. Also find the final temperature of the gas. 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 h=1.6 m; T₂=364 K. Therefore the correct answer is A.