(a)
The net work done by the gas.
(a)
Answer to Problem 73AP
The net work done by the gas is
Explanation of Solution
In the figure P22.73, the curve
Write the expression for the work done on the gas during path
Here,
Write the expression for the work done on the gas during path
Here,
Since the process along
Here,
Write the expression for the total work done on the gas.
Conclusion:
From figure,
Substitute
Substitute
Substitute
Therefore, the net work done by the gas is
(b)
The energy added to the gas by heat.
(b)
Answer to Problem 73AP
The energy added to the gas by heat is
Explanation of Solution
In figure
Write the expression for the heat absorbed by the gas in isothermal process.
Here,
Substitute
Write the expression for the specific heat capacity at constant volume of monoatomic gas.
Here,
Write the expression for the specific heat capacity at constant pressure of monoatomic gas.
Here,
Apply ideal gas equation at point
Here,
Rearrange above equation to get
Since
Here,
Substitute
Apply ideal gas equation at point
Here,
Write the expression for the energy absorbed by heat during
Here,
Write the expression for the total energy absorbed by heat.
Here,
Conclusion:
Substitute
Substitute
Since
Substitute
Substitute
Substitute
Therefore, the energy added to the gas by heat is
(c)
The energy exhausted from the gas by heat.
(c)
Answer to Problem 73AP
The energy exhausted from the gas by heat is
Explanation of Solution
Write the expression for the energy exhausted from the gas by heat.
Here,
The specific heat capacity of the gas at constant pressure is
Substitute
Apply ideal gas equation during the isobaric process
Substitute (XVII) in equation (XVI) to get
Conclusion:
Substitute
Then energy exhausted from the gas by heat is,
Therefore, the energy exhausted from the gas by heat is
(d)
The efficiency of the cycle.
(d)
Answer to Problem 73AP
The efficiency of the cycle is
Explanation of Solution
Write the expression for the efficiency of the cycle.
Here,
The total heat exhausted is equal to the sum of the heat liberated through the process described by the curves
Write the expression for the total heat exhausted at hot reservoir.
Substitute (XX) in (XIX) to get
Conclusion:
From part(b),
Substitute
Convert
Therefore the efficiency of the cycle is
(e)
The comparison for the efficiency of the engine with efficiency of Carnot engine operating between same temperature extremes.
(e)
Answer to Problem 73AP
The efficiency of the cycle is much lower than that of a Carnot engine operating between the same temperature extremes.
Explanation of Solution
The temperature of the cold reservoir is equal to temperature at point
From part(a).
Write the expression for the efficiency Carnot engine.
Here,
Conclusion:
Substitute
Efficiency of the cycle is only
Compared to efficiency of Carnot engine , efficiency of the cycle is much lower.
Therefore, the efficiency of the cycle is much lower than that of a Carnot engine operating between the same temperature extremes.
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Chapter 22 Solutions
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