Acarnot heat engine receives heat at 750°c and rejects the waste heat to the environment at 30°c. the entire work output of the heat engine is used to drive a carnot refrigerator that removes heat from the cooled space at -25°c at a rate of 300 kj/min and rejects it to the same environment at 30°c. determine: i. the thermal efficiency of the heat engine ii. the coefficient of performance of the refrigerator iii. the work input to the refrigerator iv. the minimum rate of heat supply to the heat engine, and v. the total rate of heat rejection.

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 the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct.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.