Chapter 3 Heat Engines

CHAPTER 3 HEAT ENGINES Questions and Problems 1. A typical room temperature is 68°F. What are the corresponding Celsius and Kelvin temperatures?

2. The basic equation of carbon burning is C+O2→CO2 + 95 kilocalories per mole (1 mole of carbon is 12 grams). From this equation calculate the number of Btu from burning one ton of coal, assuming it is pure carbon.

3. BONUS Starting from the Principle of Energy Conservation, explain the reasoning that gives us the

expression for thermodynamic efficiency, η, in terms of the temperatures Tc and Th. You may assume the

Carnot relation, Qc/Qh=Tc/Th, for an ideal heat engine. What is a heat engine?

4. An inventor claims to have developed a wonderful new heat engine that operates with a relatively cool (and therefore nonpolluting) flame at 150°C and discharges waste heat to the environment at 20°C. His promotional literature advertises that 45% of the fuel energy is converted into useful work. Calculate the maximum efficiency that can be expected for such an engine and compare it to the inventor's claim.

5. BONUS Because individual natural gas-fueled water heaters in homes do not have air pollution control devices, it has been proposed that water in homes be heated with electrical energy generated at a distant power plant that is equipped with effective air pollution control devices. The power plant burns natural gas and produces electrical energy with 40% efficiency; the electric transmission line between the plant and the home loses 10% of the electrical energy as heat. All that remains goes into heating the water. In contrast, the water heater gets only 60% of the fuel energy into the water. Which scheme uses more natural gas to heat a given quantity of water?

6. Why are fossil fuel-burning electric power plants situated near lakes or rivers or provided with cooling towers?

7. BONUS List the relative virtues of gasoline, diesel, and turbine types of internal combustion engines.

8. BONUS This morning, a 1−kW electric heater was switched on for one hour. Trace back as far as you can the various forms the energy had before it was used for heat. Assume a coal-fired power plant. Now trace the path the electric energy will take after it has been used for heat. What will be its ultimate destiny?

9. An electrically powered heat pump can deliver more energy than it draws from the power line without violating the Principle of Energy Conservation. Explain how this can happen.

10. SKIP

11. BONUS A heat engine in each cycle extracts 50,000 Btu of thermal energy and rejects (or releases) 20,000 Btu of thermal energy. How many Btu of work are done each cycle? What is the efficiency of this engine?

12. Show that the combination of a 40% efficient power plant with a heat pump having a coefficient of performance of 4.0 would actually deliver 60% more heat energy than if the fuel were used directly to heat a house with 100% efficiency.

13. BONUS Considering the above problem, in the interest of conserving the fossil fuel energy resource and reducing pollution, should it be unlawful to burn fossil fuels directly in the home or factory for heat? 14. A heat engine operating between a geothermal steam source at 210°C and a river at 20°C achieves an efficiency of 20%. What percentage of its theoretical maximum efficiency is it achieving?

15. A refrigerator has an energy efficiency ratio (EER) of 10. For each unit of input energy (W), drawn from

the electric power company, how many units of heat energy (Qc) are removed from the cold box, and how

many are delivered to the room (Qh)?

16. A heat pump delivers 8 Btu of heat energy to a house for each 6 Btu of heat energy that it draws from its low temperature reservoir. What is its coefficient of performance?

Multiple Choice Questions

1. For an ideal heat engine, according to Carnot:

a. ThTc=QcQh

b. TcTh=QcQh

c. ThQc=TcQh

d. TcQc=QhTh

2. BONUS For a heat pump in normal operation:

a. Qh > Qc

b. Qc > Qh

c. W = Qh

d. W > Qh

3. BONUS One hundred degrees Fahrenheit is the same as ___ degrees Kelvin.

c. 273

d. 311

4. One gram molecular weight of octane, C8H18, has a mass of ___ grams.

d. 114

e. 146

f. 224

5. How many tonnes (metric ton) of coal must be burned per day by an electric power plant that delivers 500 MWe continuously if the efficiency is 30%?

a. 1412

b. 4650

c. 8560

d. 9416

6. If an ordinary household refrigerator is left operating in a closed, perfectly insulated room with the refrigerator door standing open, after a long time, the temperature in the room will ______

a. go up b. go down

c. remain constant

d. fluctuate

7. Bonus A temperature of 98.6 degrees Fahrenheit corresponds to ___ degrees Celsius and ___ degrees Kelvin.

a. 346, 73

b. 73, 346

c. 393, 120

d. 120, 393

e. 328, 55

f. 55, 328

g. 310, 37

h. 37, 310

8. BONUS The maximum efficiency of a heat engine that has steam injected into it at 850°C and that rejects the steam at 225°C is ______

a. 74%

b. 56%

c. 44%

d. 20%

9. What is the Carnot efficiency for a heat engine that has steam injected into it at 1000°C and exhausted at 450°C?

a. 86%

b. 21%

c. 67%

d. 43%

10. For an ideal heat engine operating between thermal reservoirs at Th = 1000 C and Tc = 110°C, the efficiency is ___

a. 10%

b. 29%

c. 70%

d. 90%

e. 92%

f. 95%

g. 98%

h. cannot be determined from information given

11. A typical efficiency for a coal-burning electric power plant is ______

b. 10%

c. 25%

d. 33%

e. 66% 12. A heat engine_____

a. pumps energy "uphill"

b. is identical in function to a heat pump

c. can produce work from a temperature difference

d. can occasionally violate the first law of thermodynamics

e. is only an idea not yet achieved

13. BONUS Compare an ideal heat pump operating between Th = 100 °F and Tc = 0 °F to one operating

between Th = 100 °F and Tc = 45 °F. In the second case, the Coefficient of Performance is _____ times larger than for the first.

a. 0.9

b. 1.8

c. 3.6

d. 7.2

e. 14.4

14. SKIP

15. BONUS The total rate of energy use in the United States is now such that each person has the equivalent of about _____ horsepower working continuously.

a. 0.015

b. 0.15

c. 1.5

e. 150

f. 1500

16. The methane in natural gas burns according to CH4 + 2 O2 → CO2 → 2 H2O. How many tons of CO2 are produced for each ton of methane that is burned?

a. 2.75

b. 3.7

17. Which one of the following is not a heat engine?

a. an internal combustion auto engine

b. 100 horsepower electric motor

c. a 2000 horsepower jet aircraft engine

d. an 800 pound diesel truck engine

e. a Saturn V rocket

18. BONUS The Principle of Energy Conservation is

a. frequently violated by practical devices

b. one of the laws of thermodynamics c. an exception to Carnot efficiency

d. correct only on the Kelvin temperature scale

e. correct only on the Celsius temperature scale

f. a violation of the laws of thermodynamics

19. Bonus The Coefficient of Performance for a good heat pump is ______

a. a negative number

b. equal to the number 1.0

c. larger for smaller temperature difference

d. smaller for smaller temperature difference

e. not a numerical quantity

f. meaningless

20. A power plant having an efficiency of 30% burns 7200 tonnes of coal per day. The coal produces 2 × 104 Btu/kg. What is the electric power output of the plant in kilowatts? 3 a. 2.75×10 2 b. 7.25×10 7 c. 6.25×10 6 d. 5.72×10 4 e. 6.75×10 5 f. 5.27×10

21. Bonus Cogeneration ______

a. is a vague dream not yet proven to be practical

b. would increase a nation's demands on fuel resources

c. might work for a small factory but not for a large institution

d. offers considerable promise of reducing a nation's energy waste

e. will probably increase thermal pollution of rivers