(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 Scientists and Engineers with Modern Physics, Technology Update
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