Tutorial: Second Law of Thermodynamics

TUTORIAL: SECOND LAW OF THERMODYNAMICS

Problem 1 A heat engine that pumps water out of an underground mine accepts 500 kJ of heat and produces 200 kJ of work. How much heat does it reject, in kJ?

Problem 2. A steam power plant with a power output of 150 MW consumes coal at a rate of 60 tons/h. If the heating value of the coal is 30,000 kJ/kg. determine the overall efficiency of this plany. Ans. 30 percent

Problem 3. An automobile engine consumes fuel at a rate of 28 L/h and delivers 60 kW of power to the wheels. If the fuel has a heating value of 44,000 kJ/kg and the density of 0.8 g/cm3, determine the efficiency of this engine. Ans. 21.9 percent

Problem 4. A household refrigerator with a COP of 1.2 removes heat from the refrigerated space at a rate of 60 kJ/min. Determine (a) the electric power consumed by the refrigerator and (b) the rate of heat transfer to the kitchen air. Ans. (a) 0.83 kW, (b) 110 kJ/min

Problem 5. A commercial heat pump removes 10,000 kJ/h from the source, rejects 15,090 kJ/h to the sink, and requires 1.5 kW of power. What is this heat pump’s coefficient of performance?

Problem 6. A household refrigerator that has a power input of 450 W and a COP of 2.5 is to cool five large watermelons, 10 kg each, to 8 oC. If the watermelons are initially at 20 oC, determine how long it will take for the refrigerator to cool them. The watermelons can be treated as water whose specific heat is 4.2 kJ/kg.oC. Ans. 2240 s

Problem 7. A heat pump is used to maintain a house at a constant temperature of 23 oC. The house is losing heat to the outside air through the walls and the windows at a rate of 60, 000 kJ/h while the energy generated within the house from people, lights, and appliances amounts to 4,000 kJ/h. For a COP of 2.5, determine the required power input to the heat pump. Ans. 6.22 kW

Problem 8. A heat engine operates between a source at 550 oC and a sink at 25 oC. If heat is supplied to the heat engine at a steady rate of 1200 kJ/min, determine the maximum power output of this heat engine.

Problem 9. A completely reversible heat engine operates with a source at 800 K and a sink at 280 K. At what rate must heat be supplied to this engine, in kJ/h, for it to produce 4 kW of power? Ans. 22,150 kJ/h Problem 10. An inventor claims to have developed a heat engine that receives 700 kJ of heat from a source at 500 K and produces 300 kJ of net work while rejecting the waste heat to a sink at 290 K. Is this a reasonable claim? Why?

Problem 11. A thermodynamicist claims to have developed a heat engine with 50 percent thermal efficiency when operating with thermal energy reservoirs at 700 K and 280 K. Is this claim valid?

Problem 12. A completely reversible refrigerator is driven by a 10 kW compressor and operates with thermal energy reservoirs at 250 K and 300 K. Calculate the rate of cooling provided by this refrigerator. Ans. 50 kW