A cylinder with a movable piston contains n moles of gas at a temperature higher than that of the surrounding environment. An external force on the piston keeps the pressure constant while the gas cools as ΔT = (ΔT)₀^e-t/τ, where ΔT is the temperature difference between the gas and the environment, (ΔT)₀ is the initial temperature difference, and t is the time constant.
a. Find an expression for the rate at which the environment does work on the gas. Recall that the rate of doing work is power.
b. What power is initially supplied by the environment if 0.15 mol of gas are initially 12°C warmer than the surroundings and cool with a time constant of 60 s?