Problems
Heat Engines
An engine that operates between two reservoirs at TH = 500 ◦C and TL = 25 ◦C produces 1 MW of power from a heat intake of 2.5 MW. Compute the heat rejected, the thermal efficiency, the entropy generation rate, and the work loss to irreversibilities.
Another engine operates between two reservoirs at TH = 1000 ◦C and TL = 10 ◦C, and has a thermal efficiency of 45% and its heat rejection rate is 1.76 MW. Compute the power produced, the heat intake rate, the entropy generation rate, and the work loss to irreversibilities.
Investment Advice
A friend asks whether he should invest in a new start-up company. The company claims to sell a power generation device that produces 12.5 kW of power, takes in 21 kW of heat at a temperature of 800 K and rejects 13 kW of heat at 300 K. What advice do you give? Why?
More Investment Advice
Another friend asks whether she should invest in a company which claims to make a power generation device that produces 12 kW of power, takes in heat at a temperature of 800 K and rejects 8 kW of heat at 350 K. What advice do you give? Why?
Your Friends Keep Asking You for Advice
A neighbor would like to have an air conditioning system. He finds a product with the following specifications: For keeping a room at 20 ◦C when the outside temperature is 30 ◦C the product consumes 0.5 kW to remove 9 kW of heat. What’s your advice here, and why?
The Perfect Heater?
A relative needs a new heating system. She shows you a flyer from a company marketing baseboard heaters. The flyer claims a 100% heating efficiency. Is that a valid claim? Can your relative find a more efficient alternative? If so, what would it be?
A Refrigerator
Yet another friend asks whether he should invest in a company which claims to produce a refrigeration device with a COP of 7, that consumes 0.9 kW of power to keep the inside at 4 ◦C, and rejects of heat to the warm environment at 32 ◦C. What advice do you give? Why?
A Heat Pump
An off-the shelf heat pump system has a COP of 3.5 for operation between 30 ◦C and −10 ◦C. Determine the entropy generation per kW of heating, and the percentage of consumed power required to overcome irreversibilities.
Another Heat Pump
A heat pump providing 2 kW of heat operates between the temperatures of 23 ◦C and −2 ◦C ; its entropy generation rate is S˙gen = 1.3 W . Determine the power needed to drive the heat pump, and its COP.
Heat Engine with External Irreversibilities
A internally reversible heat engine operates between two reservoirs at 300 K and 400 K; the engine produces 40 kW of power. The heat exchangers between the engine and the reservoirs require a temperature difference of 20 K. Deter- mine the heat exchanged with the two environments, the entropy generated in heat transfer, and the work loss.
Refrigerator with Internal and External Irreversibilities
In a frozen pizza factory, the freezing compartment is kept at a temperature of −30 ◦C, while the outside temperature is 25 ◦C. The cooling system removes 2.25 MW of heat, and consumes 1.5 MW of power. Measurements show that both heat exchangers operate at a temperature difference of 12 ◦C to their respective environments.
1. Determine the COP of the refrigeration system, and the COP and power requirement of a fully reversible system used for the same cooling purpose.
2. Determine the work losses to internal and external irreversibilities.
Heat for Cooling
A chemical plant rejects 1 MW of waste heat at 400 ◦C. Elsewhere in the plant, 5 MW of heat have to be removed from a warehouse at −10 ◦C. Can the waste heat be used to cool the warehouse when the environment is at 17 ◦C? If so, how? Give arguments based on 1st and 2nd law, discuss your assumptions.
Entropy Generation
In an industrial process, a device conducts heat between two hot reservoirs, which are at 200 ◦C and 400 ◦C, and the environment at 23 ◦C. Specifically, the conductor exchanges 4 kW of heat with the hottest reservoir, and 6 kW of heat with the environment. Determine the entropy generation, and the respective work loss.
Heat in the T-S-Diagram
