A 1.00-mol sample of an ideal monatomic gas is taken through the cycle shown in Figure P21.37. The process A → B 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 P21.37
(a)
The net work done by the gas.
Answer to Problem 22.73AP
The net work done by the gas is
Explanation of Solution
The pressure and volume at A are
Write the formula for the net work done by the gas at
Here,
Substitute
Write the formula for the net work done by the gas at
Here,
Substitute
Write the formula for the net work done by the gas at
As the change in the volume during processes
Write the formula for the total work done by the gas
Conclusion:
Substitute
Therefore, the total work done is
(b)
The energy added to the gas by heat.
Answer to Problem 22.73AP
The energy added to the gas by heat is
Explanation of Solution
The pressure and volume at
The formula for the energy added by the gas in process
Substitute
Thus, the energy added by the gas in process
Write the formula for temperature at
Substitute
Write the formula for temperature at
Substitute
Write the formula for the energy added by the gas in process
Here,
Substitute
Write the formula for the total energy added
Conclusion:
Substitute
Thus, the total energy added is
(c)
The energy exhausted from the gas by heat.
Answer to Problem 22.73AP
The energy exhausted from the gas by heat is
Explanation of Solution
The pressure and volume at A are
Write the formula for the energy added by the gas in process
Conclusion:
Substitute
Thus, the energy exhausted in process
(d)
The efficiency of the cycle.
Answer to Problem 22.73AP
The efficiency of the cycle is
Explanation of Solution
The pressure and volume at A are
Write the formula to calculate the efficiency of the engine
Here,
Conclusion:
Substitute
Thus, the efficiency of the engine is
(e)
The comparison of efficiency to that of the Carnot engine.
Answer to Problem 22.73AP
The efficiency of Carnot engine is
Explanation of Solution
The pressure and volume at A are
Write the formula to calculate the efficiency of the Carnot engine
Conclusion:
Substitute
Therefore, the efficiency of Carnot engine is
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- An 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_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
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