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 37AP
The net work done by the gas is
Explanation of Solution
Given Info: The pressure and volume at A are
The formula for the net work done by the gas at
Here,
Substitute
Thus, the net work done by the gas at
The formula for the net work done by the gas at
Here,
Substitute
Thus, the net work done by the gas at BC is
The formula for the net work done by the gas at
As the change in the volume between processes
Thus, the net work done by the gas at
The formula for the total work done by the gas is,
Substitute
Conclusion:
Therefore, the total work done is
(b)
The energy added to the gas by heat.
Answer to Problem 37AP
The energy added to the gas by heat is
Explanation of Solution
Given Info: 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
The formula for temperature at
Substitute
Thus, the temperature at
The formula for temperature at
Substitute
Thus, the temperature at
The formula for the energy added by the gas in process
Here,
Substitute
Thus, the energy added in process
The formula for the total energy added is,
Substitute
Thus, the total energy added is
Conclusion:
Therefore, the total energy added is
(c)
The energy exhausted from the gas by heat.
Answer to Problem 37AP
The energy exhausted from the gas by heat is
Explanation of Solution
Given Info: The pressure and volume at A are
The formula for the energy added by the gas in process
Substitute
Thus, the energy exhausted in process
Conclusion:
Therefore, the energy exhausted in process
(d)
The efficiency of the cycle.
Answer to Problem 37AP
The efficiency of the cycle is
Explanation of Solution
Given Info: The pressure and volume at A are
Formula to calculate the efficiency of the engine is,
Here,
Substitute
Thus, the efficiency of the engine is
Conclusion:
Therefore, the efficiency of the engine is
(e)
The comparison of efficiency to that of the Carnot engine.
Answer to Problem 37AP
The efficiency of Carnot engine is
Explanation of Solution
Given Info: The pressure and volume at A are
Formula to calculate the efficiency of the Carnot engine is,
Substitute
Conclusion:
Therefore, the efficiency of Carnot engine is
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