At a steady state, a thermodynamic cycle operating between hot and cold reservoirs at 1000K ands respectively. The cycle receives energy by heat transfer from the hot reservoir at a rate of 1500kW, and discharges energy by heat transfer to the cold reservoir. The cycle develops power at a rate of (a)0 (b) 250 kW and ()1000kW For each case, based on the Clausius inequality, determine whether the cycle operates reversibly, irreversibly or is impossible.

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.