b) Find an expression for the efficiency of this cycle in terms of only the compression ratio. c) If state a is at room temperature (300 K) and atmospheric pressure (100 kPa), and the compression ratio is 4, what is the efficiency for this heat engine? Question 8: A new heat engine cycle can be described by an adiabatic compression (a → b), an isothermal expansion (b → c), and an isochoric cooling process (c → a), as shown in the graph. The compression ratio is r. For a diatomic ideal gas: Cv = 5R/2, Cp = 7R/2, y = 1.4 Assume the processes are reversible. a) Write down the expressions (not the values) for the heat transferred during each process. Pressure b Vo 0 r Vo Volume a

b) Find an expression for the efficiency of this cycle in terms of only the compression ratio. c) If state a is at room temperature (300 K) and atmospheric pressure (100 kPa), and the compression ratio is 4, what is the efficiency for this heat engine? Question 8: A new heat engine cycle can be described by an adiabatic compression (a → b), an isothermal expansion (b → c), and an isochoric cooling process (c → a), as shown in the graph. The compression ratio is r. For a diatomic ideal gas: Cv = 5R/2, Cp = 7R/2, y = 1.4 Assume the processes are reversible. a) Write down the expressions (not the values) for the heat transferred during each process. Pressure b Vo 0 r Vo Volume a

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter22: Heat Engines, Entropy, And The Second Law Of Thermodynamics

Section: Chapter Questions

Problem 22.4OQ: Of the following, which is not a statement of the second law of thermodynamics? (a) No heat engine...

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Of 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.
(a) What is the hot reservoir temperature of a Carnot engine that has an eficiency of 42.0% and a cold reservoir temperature of 210C ? (b) What must the hot reservoir temperature be for a real heat engine that achieves 0.700 of the maximum eficiency, but still has an efficiency of 42.0% (and a cold reservoir at 27.0C )? (c) Does your answer imply practical limits to the efficiency of car gasoline engines?
(a) On a winter day, a certain house loses 5.00108J of heat to the outside (about 500,000 Btu). What is the total change in entropy due to this heat transfer alone, assuming an average indoor temperature of 21.0C and an average outdoor temperature of 5.00C ? (b) This large change in entropy implies a large amount of energy has become unavailable to do work. Where do we find more energy when such energy is lost to us?
At point A in a Carnot cycle, 2.34 mol of a monatomic ideal gas has a pressure of 1 4000 kPa, a volume of 10.0 L, and a temperature of 720 K. The gas expands isothermally to point B and then expands adiabatically to point C, where its volume is 24.0 L. An isothermal compression brings it to point D, where its volume is 15.0 L. An adiabatic process returns the gas to point A. (a) Determine all the unknown pressures, volumes, and temperatures as you f ill in the following table: (b) Find the energy added by heat, the work done by the engine, and the change in internal energy for each of the steps A B, B C, C D, and D A (c) Calculate the efficiency Wnet/|Qk|. (d) Show that the efficiency is equal to 1 - TC/TA, the Carnot efficiency.
(a) How much heat transfer occurs from 20.0 kg of 90.0C water placed in contact with 20.0 kg of 10.0C water, producing a final temperature of 50.0C ? (b) How much work could a Carnot engine do with this heat transfer, assuming it operates between two reservoirs at constant temperatures of 90.0C and 10.0C ? (c) What increase in entropy is produced by mixing 20.0 kg of 90.0C water with 20.0 kg of 10.0C water? (d) Calculate the amount of work made unavailable by this mixing using a low temperature of 10.0C, and compare it with the work done by the Garnet engine. Explicitly show how you follow the steps in the Problem-Solving Strategies for Entropy. (e) Discuss how everyday processes make increasingly more energy unavailable to do work, as implied by this problem.
Figure P22.73 illustrates the cycle ABCA for a 2.00-mol sample of an ideal diatomic gas, where the process CA is a reversible isothermal expansion. What is a. the net work done by the gas during one cycle? b. How much energy is added to the gas by heat during one cycle? c. How much energy is exhausted from the gas by heat during one cycle? d. What is the efficiency of the cycle? e. What would be the efficiency of a Carnot engine operated between the temperatures at points A and B during each cycle?
(a) What is the change in entropy if you start with 10 coins in the 5 heads and 5 tails macrostate, toss them, and get 2 heads and 8 tails? (b) How much more likely is 5 heads and 5 tails than 2 heads and 8 tails? (Take the ratio of the number of microstates to find out.) (c) If you were betting on 2 heads and 8 tails would you accept odds of 252 to 45? Explain Why or why not. Table 15.5 10Coin Toss MacrostateNumber of Microstates (W) Heads Tails 10 0 1 9 1 10 8 2 45 7 3 120 6 4 210 5 5 252 4 6 210 3 7 120 2 8 45 1 9 10 0 10 1 Total: 1024
(a) In reaching equilibrium, how much heat transfer occurs from 1.00 kg of water at 40.0C when it is placed in contact with 1.00 kg of 20.0C water in reaching equilibrium? (b) What is the change in entropy due to this heat transfer? (c) How much work is made unavailable, taking the lowest temperature to be 20.0C ? Explicitly show how you follow the steps in the Problem-Solving Strategies for Entropy.
(a) What is the change in entropy if you start with 100 coins in the 45 heads and 55 tails macrostate, toss them, and get 51 heads and 49 tails? (b) What if you get 75 heads and 25 tails? (c) How much more likely is 51 heads and 49 tails than 75 heads and 25 tails? (d) Dues either outcome violate the second law of thermodynamics?
A Carnot engine employs 1.5 mol of nitrogen gas as a working substance, which is considered as an ideal diatomic gas with =7.5 at the working temperatures of the engine. The Carnot cycle goes in the cycle ABCDA with AB being an isothermal expansion. The volume at points A and C of the cycle are 5.0103 m3 and 0.15 L, respectively. The engine operates between two thermal baths of temperature 500 K 300 K. (a) Find the values of volume at B and D. (b) How much heat is absorbed by the gas in the AB isothermal expansion? (c) How much work is done by the gas in the AB isothermal expansion? (d) How much heat is given up by the gas in the CD isothermal expansion? (e) How much work is done by the gas in the CD isothermal compression? (f) How much work is done by the gas in the BC adiabatic expansion? (g) How much work is done by the gas in the DA adiabatic compression? (h) Find the value of efficiency of the engine based on the net and heat input. Compare this value to the efficiency of a Carnot engine based on the temperatures of the baths.
A sample of a monatomic ideal gas is contained in a cylinder with a piston. Its stale is represented by the dot in the PV diagram shown in Figure OQ22.9. Arrows A through E represent isobaric, isothermal, adiabatic, and isovolumetric processes that the sample can undergo. In each process except D, the volume changes by a factor of 2. All five processes are reversible. Rank the processes according to the change in entropy of the gas from the largest positive value to the largest-magnitude negative value. In your rankings, display any cases of equality.
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).