(a)
The total energy entering the system by heat per cycle.
(a)
Answer to Problem 76AP
The total energy entering the system by heat per cycle is
Explanation of Solution
Apply ideal gas equation at the point A.
Here,
Apply ideal gas equation at the point B.
Here,
Substitute
Apply ideal gas equation at the point C.
Here,
Substitute
Apply ideal gas equation at the point D.
Here,
Substitute
From figure P22.76, the curve
Write the expression for the heat change during process defined by curve
Here,
From figure P22.76, the curve
Write the expression for the heat change during process defined by curve
Here,
From figure P22.76, the curve
Write the expression for the heat change during process defined by curve
Here,
From figure P22.76, the curve
Write the expression for the heat change during process defined by curve
Here,
In this cycle heat is entering through process
Write the expression for the total heat entering the cycle.
Here,
This heat entering must be equal to heat absorbed from hot reservoir by the gas.
Here,
Conclusion:
The specific heat capacity at constant volume of the monoatomic gas is
Substitute
Substitute
Substitute
Therefore, the total energy entering the system by heat per cycle is
(b)
The total energy leaving the system by heat per cycle.
(b)
Answer to Problem 76AP
The total energy leaving the system by heat per cycle is
Explanation of Solution
In this cycle heat is leaving through processes
Write the expression for the heat leaving the system.
Here,
This heat leaving must be equal to heat expelled to cold reservoir by the gas.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the total energy leaving of an engine operating in this cycle is
(c)
The efficiency of the engine operating in this cycle.
(c)
Answer to Problem 76AP
The efficiency of the engine operating in this cycle is
Explanation of Solution
Write the expression for the efficiency of the engine.
Here,
Substitute
Substitute
Conclusion:
Put the above two equations in equation (XVI) to find
Therefore, the efficiency of the engine operating in this cycle is
(d)
The comparison between actual efficiency of the engine and Carnot efficiency.
(d)
Answer to Problem 76AP
The Carnot efficiency of the engine is
Explanation of Solution
Write the expression for the Carnot efficiency.
Here,
Conclusion:
Substitute
Therefore, Carnot efficiency is
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Chapter 22 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
- A 1.00-mol sample of a monatomic ideal gas is taken through the cycle shown in Figure P22.76. At point A, the pressure, volume, and temperature are Pi, Vi, and Ti, respectively. In terms of R and Ti, find (a) the total energy entering the system by heat per cycle, (b) the total energy leaving the system by heat per cycle, and (c) the efficiency of an engine operating in this cycle. (d) Explain how the efficiency compares with that of an engine operating in a Carnot cycle between the same temperature extremes.arrow_forwardA 1.00-mol sample of an ideal monatomic gas is taken through the cycle shown in Figure P18.63. The process AB is a reversible isothermal expansion. Calculate (a) the net work done by the gas, (b) the energy added to the gas by heat, (c) the energy exhausted from the gas by heat, and (d) the efficiency of the cycle. (e) Explain how the efficiency compares with that of a Carnot engine operating between the same temperature extremes. Figure P18.63arrow_forwardAn ideal gas with specific heat ratio confined to a cylinder is put through a closed cycle. Initially, the gas is at Pi, Vi, and Ti. First, its pressure is tripled under constant volume. It then expands adiabatically to its original pressure and finally is compressed isobarically to its original volume. (a) Draw a PV diagram of this cycle. (b) Determine the volume at the end of the adiabatic expansion. Find (c) the temperature of the gas at the start of the adiabatic expansion and (d) the temperature at the end of the cycle. (e) What was the net work done on the gas for this cycle?arrow_forward
- Figure P21.45 shows a cyclic process ABCDA for 1.00 mol of an ideal gas. The gas is initially at Pi = 1.50 105 Pa, Vi = 1.00 103 m3 (point A in Fig. P21.45). a. What is the net work done on the gas during the cycle? b. What is the net amount of energy added by heat to this gas during the cycle? FIGURE P21.45arrow_forwardFigure 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?arrow_forwardA thermodynamic cycle is shown in Figure P21.34 for a gas in a piston. The system changes states along the path ABCA. a. What is the total work done by the gas during this cycle? b. How much heat is transferred? Does heat flow into or out of the system? Figure P21.34arrow_forward
- 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.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_forwardConsider the cyclic process depicted in Figure P17.28. If Q is negative for the process BC and Eint is negative for the process CA, what are the signs of Q, W, and Eint that are associated with each of the three processes?arrow_forward
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