EBK PHYSICS FOR SCIENTISTS AND ENGINEER
9th Edition
ISBN: 9780100460300
Author: SERWAY
Publisher: YUZU
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Chapter 22, Problem 22.20P
An ideal refrigerator or ideal heat pump is equivalent to a Carnot engine running in reverse. That is, energy |Qc| is taken in from a cold reservoir and energy |Qh| is rejected to a hot reservoir. (a) Show that the work that must he supplied to run the refrigerator or heat pump is
(b) Show that the coefficient of performance (COP) of the ideal refrigerator is
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An ideal refrigerator or ideal heat pump is equivalent to a
Carnot engine running in reverse. That is, energy |Q] is
taken in from a cold reservoir and energy |Q,| is rejected
to a hot reservoir. (a) Show that the work that must be sup-
plied to run the refrigerator or heat pump is
Т, — т.
-
W =
T.
(b) Show that the coefficient of performance (COP) of the
ideal refrigerator is
T.
СОР
T- T.
It has been proposed to use the thermal gradient of the ocean to drive a heat engine. Suppose that at a certain location the water temperature is 22° C at the ocean surface and 40 C at the ocean floor.
(a) What is the maximum possible efficiency of an engine operating between these two temperatures? (b) If the engine is to produce 1 GW of electrical power, what minimum volume of water must be processed (to suck out the heat) in every second?
A power plant has been proposed that would make use of the temperature gradient in the ocean. The system is to operate between 20.0°C (surface water temperature) and 5.00°C (water temperature at a depth of about 1 km). (a) What is the maximum efficiency of such a system? (b) If the useful power output of the plant is 75.0 MW, how much energy is absorbed per hour? (c) In view of your answer to part (a), do you think such a system is worthwhile (considering that there is no charge for fuel)?
Chapter 22 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
Ch. 22 - The energy input to an engine is 4.00 times...Ch. 22 - The energy entering an electric heater by...Ch. 22 - Three engines operate between reservoirs separated...Ch. 22 - (a) Suppose you select four cards at random from a...Ch. 22 - An ideal gas is taken from an initial temperature...Ch. 22 - True or False: The entropy change in an adiabatic...Ch. 22 - The second law of thermodynamics implies that the...Ch. 22 - Assume a sample of an ideal gas is at room...Ch. 22 - A refrigerator has 18.0 kJ of work clone on it...Ch. 22 - Of the following, which is not a statement of the...
Ch. 22 - Consider cyclic processes completely characterized...Ch. 22 - Prob. 22.6OQCh. 22 - A steam turbine operates at a boiler temperature...Ch. 22 - A thermodynamic process occurs in which the...Ch. 22 - A sample of a monatomic ideal gas is contained in...Ch. 22 - An engine does 15.0 kJ of work while exhausting...Ch. 22 - The arrow OA in the PV diagram shown in Figure...Ch. 22 - The energy exhaust from a certain coal-fired...Ch. 22 - Discuss three different common examples of natural...Ch. 22 - Prob. 22.3CQCh. 22 - The first law of thermodynamics says you cant...Ch. 22 - Energy is the mistress of the Universe, and...Ch. 22 - Prob. 22.6CQCh. 22 - The device shown in Figure CQ22.7, called a...Ch. 22 - A steam-driven turbine is one major component of...Ch. 22 - Discuss the change in entropy of a gas that...Ch. 22 - Prob. 22.10CQCh. 22 - Prob. 22.11CQCh. 22 - (a) If you shake a jar full of jelly beans of...Ch. 22 - Prob. 22.13CQCh. 22 - A particular heat engine has a mechanical power...Ch. 22 - The work done by an engine equals one-fourth the...Ch. 22 - A heat engine takes in 360 J of energy from a hot...Ch. 22 - A gun is a heat engine. In particular, it is an...Ch. 22 - An engine absorbs 1.70 kJ from a hot reservoir at...Ch. 22 - A multicylinder gasoline engine in an airplane,...Ch. 22 - Suppose a heat engine is connected to two energy...Ch. 22 - A refrigerator has a coefficient of performance...Ch. 22 - During each cycle, a refrigerator ejects 625 kJ of...Ch. 22 - A heat pump has a coefficient of performance of...Ch. 22 - A refrigerator has a coefficient of performance of...Ch. 22 - A heat pump has a coefficient of performance equal...Ch. 22 - A freezer has a coefficient of performance of...Ch. 22 - Prob. 22.14PCh. 22 - One of the most efficient heat engines ever built...Ch. 22 - Why is the following situation impossible? An...Ch. 22 - A Carnot engine has a power output of 150 kW. The...Ch. 22 - A Carnot engine has a power output P. The engine...Ch. 22 - What is the coefficient of performance of a...Ch. 22 - An ideal refrigerator or ideal heat pump is...Ch. 22 - Prob. 22.21PCh. 22 - How much work does an ideal Carnot refrigerator...Ch. 22 - If a 35.0% -efficient Carnot heat engine (Fig....Ch. 22 - A power plant operates at a 32.0% efficiency...Ch. 22 - A heat engine is being designed to have a Carnot...Ch. 22 - A Carnot heat engine operates between temperatures...Ch. 22 - An ideal gas is taken through a Carnot cycle. The...Ch. 22 - Prob. 22.28PCh. 22 - Prob. 22.29PCh. 22 - Suppose you build a two-engine device with the...Ch. 22 - Argon enters a turbine at a rate of 80.0 kg/min, a...Ch. 22 - At point A in a Carnot cycle, 2.34 mol of a...Ch. 22 - An electric generating station is designed to have...Ch. 22 - An ideal (Carnot) freezer in a kitchen has a...Ch. 22 - A heat pump used for heating shown in Figure...Ch. 22 - A gasoline engine has a compression ratio of 6.00....Ch. 22 - In a cylinder of an automobile engine, immediately...Ch. 22 - An idealized diesel engine operates in a cycle...Ch. 22 - Prob. 22.39PCh. 22 - (a) Prepare a table like Table 21.1 for the...Ch. 22 - Prob. 22.41PCh. 22 - An ice tray contains 500 g of liquid water at 0C....Ch. 22 - A Styrofoam cup holding 125 g of hot water at 100C...Ch. 22 - A 1.00-kg iron horseshoe is taken from a forge at...Ch. 22 - A 1 500-kg car is moving at 20.0 m/s. The driver...Ch. 22 - Prob. 22.46PCh. 22 - Prob. 22.47PCh. 22 - 1.00-mol sample of H2 gas is contained in the left...Ch. 22 - A 2.00-L container has a center partition that...Ch. 22 - What change in entropy occurs when a 27.9-g ice...Ch. 22 - Calculate the change in entropy of 250 g of water...Ch. 22 - How fast are you personally making the entropy of...Ch. 22 - When an aluminum bar is connected between a hot...Ch. 22 - When a metal bar is connected between a hot...Ch. 22 - Prob. 22.55PCh. 22 - Calculate the increase in entropy of the Universe...Ch. 22 - How much work is required, using an ideal Carnot...Ch. 22 - Prob. 22.58APCh. 22 - The energy absorbed by an engine is three times...Ch. 22 - Prob. 22.60APCh. 22 - Prob. 22.61APCh. 22 - In 1993, the U.S. government instituted a...Ch. 22 - Prob. 22.63APCh. 22 - One mole of neon gas is heated from 300 K to 420 K...Ch. 22 - Au airtight freezer holds n moles of air at 25.0C...Ch. 22 - Suppose an ideal (Carnot) heat pump could be...Ch. 22 - In 1816, Robert Stirling, a Scottish clergyman,...Ch. 22 - A firebox is at 750 K, and the ambient temperature...Ch. 22 - Review. This problem complements Problem 44 in...Ch. 22 - A biology laboratory is maintained at a constant...Ch. 22 - A power plant, having a Carnot efficiency,...Ch. 22 - A power plant, having a Carnot efficiency,...Ch. 22 - A 1.00-mol sample of an ideal monatomic gas is...Ch. 22 - A system consisting of n moles of an ideal gas...Ch. 22 - A heat engine operates between two reservoirs at...Ch. 22 - A 1.00-mol sample of a monatomic ideal gas is...Ch. 22 - A sample consisting of n moles of an ideal gas...Ch. 22 - An athlete whose mass is 70.0 kg drinks 16.0...Ch. 22 - Prob. 22.79APCh. 22 - Prob. 22.80APCh. 22 - A 1.00-mol sample of an ideal gas ( = 1.40) is...Ch. 22 - The compression ratio of an Otto cycle as shown in...
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- Show that the coefficients of performance of refrigerators and heat pumps are related by COPref=COPhp1. Start with the definitions of the COP s and the conservation of energy relationship between Qh, QC, and W.arrow_forwardA copper rod of cross-sectional area 5.0 cm2 and length 5.0 m conducts heat from a heat reservoir at 373 K to one at 273 K. What is the time rate of change of the universe's entropy for this process?arrow_forwardWhich of the following is true for the entropy change of a system that undergoes a reversible, adiabatic process? (a) S 0 (b) S = 0 (c) S 0arrow_forward
- A Carnot engine has an efficiency of 0.60. When the temperature of its cold reservoir the efficiency drops to 0.55. If initially Tc=27, determine (a) the constant value of Th and (b) the final value of Tc.arrow_forwardTrue or False: The entropy change in an adiabatic process must be zero because Q = 0.arrow_forwardConsider cyclic processes completely characterized by each of the following net energy inputs and outputs. In each case, the energy transfers listed are the only ones occurring. Classify each process as (a) possible, (b) impossible according to the first law of thermodynamics, (c) impossible according to the second law of thermodynamics, or (d) impossible according to both the first and second laws. (i) Input is 5 J of work, and output is 4 J of work. (ii) Input is 5 J of work, and output is 5 J of energy transferred by heat. (iii) Input is 5 J of energy transferred by electrical transmission, and output is 6 J of work. (iv) Input is 5 J of energy transferred by heat, and output is 5 J of energy transferred by heat. (v) Input is 5 J of energy transferred by heat, and output is 5 J of work. (vi) Input is 5 J of energy transferred by heat, and output is 3 J of work plus 2 J of energy transferred by heat.arrow_forward
- Find the work done in the quasi-static processes shown below. The states are given as (p, V) values for the points in the PV plane: 1 (3 atm, 4 L), 2 (3 atm, 6 L), 3 (5 atm, 4 L), 4 (2 atm, 6 L), 5 (4 atm, 2 L), 6 (5 atm, 5 L) and 7 (2 atm, 5 L).arrow_forwardA heat engine operates between two temperatures such that the working substance of the engine absorbs 5000 J of heat from the high-temperature bath and discharges 3000 J to the low-temperature bath. The rest of the energy is converted into mechanical energy of the turbine. Find (a) the amount of work produced by the engine and (b) the efficiency of the engine.arrow_forwardOf the following, which is not a statement of the second law of thermodynamics? (a) No heat engine operating in a cycle can absorb energy from a reservoir and use it entirely to do work, (b) No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs, (c) When a system undergoes a change in state, the change in the internal energy of the system is the sum of the energy transferred to the system by heat and the work done on the system, (d) The entropy of the Universe increases in all natural processes, (e) Energy will not spontaneously transfer by heat from a cold object to a hot object.arrow_forward
- Two moles of a monatomic ideal gas such as oxygen is compressed adiabatically and reversibly from a state (3 atm, 5 L) to a state with a pressure of 4 atm. (a) Find the volume and temperature of the final state. (b) Find the temperature of the initial state. (c) Find work done by the gas in the process. (d) Find the change in internal energy in the process. Assume Cv=5R and Cp=Cv+R for the diatomic ideal gas in the conditions given.arrow_forwardWater falls over a dam of height h with a mass flow rate of R, in units of kilograms per second. (a) Show that the power available from the water is P=Rgh where g is the free-fall acceleration. (b) Each hydroelectric unit at the Grand Coulee Dam takes in water at a rate of 8.50 105 kg/s from a height of 87.0 m. The power developed by the falling water is converted to electric power with an efficiency of 85.0%. How much electric power does each hydroelectric unit produce?arrow_forwardDoes the entropy increase for a Carnot engine for each cycle?arrow_forward
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