Concept explainers
(a)
Draw the
(a)
Answer to Problem 180RP
The
Explanation of Solution
Draw the
Thus, the
(b)
The expression for the back work ratio as a function of k and r.
(b)
Answer to Problem 180RP
The expression for the back work ratio as a function of k and r is
Explanation of Solution
Find the work of compression using the first law for process 1-2.
Here, heat interaction during the process 1-2 is
Write the expression of expansion work.
Here, gas constant is R, specific volume at state 2 and 3 is
Write the expression of back work ratio using the equations (I) and (II).
Here, temperature at state 1, 2, and 3 are
Conclusion:
Process 1-2: Isentropic
Calculate the ratio of
Here, pressure at state 1 and 2 is
Process 2-3: Constant pressure
Calculate the expression for
Here, volume at state 1 and 2 is
Process 3-1: Constant volume
Calculate the expression for
Substitute
Thus, the expression for the back work ratio as a function of k and r is
(c)
The expression for the cycle thermal efficiency as a function of k and r.
(c)
Answer to Problem 180RP
The expression for the cycle thermal efficiency as a function of k and r is
Explanation of Solution
Express out the heat addition and heat rejection in the process using first law to the closed system for processes 2-3 and 3-1.
Here, constant pressure specific heat is
Express the cycle thermal efficiency.
Conclusion:
Substitute
Substitute
Thus, the expression for the cycle thermal efficiency as a function of k and r is
(d)
The value of the back work ratio and thermal efficiency as r goes to unity.
(d)
Answer to Problem 180RP
The value of the back work ratio and thermal efficiency as r goes to unity is
Explanation of Solution
Recall the expression of back work ratio and apply the limits as r goes to infinity.
Thus, the value of the back work ratio as r goes to unity is
Recall the expression of cycle thermal efficiency and apply the limits as r goes to infinity.
Thus, the value of the thermal efficiency as r goes to unity is
From the results of cycle thermal efficiency and back work ratio values of 0 and 1, it shows that no expansion and net work can be done whether you add heat to the system when there is no compression
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Chapter 9 Solutions
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