An air-standard cycle, called the dual cycle, with constant specific heats is executed in a closed piston– cylinder system and is composed of the following five processes:
1-2 Isentropic compression with a compression ratio, r = V1/V2
2-3 Constant-volume heat addition with a pressure ratio, rp = P3/P2
3-4 Constant-pressure heat addition with a volume ratio, rc V4/V3
4-5 Isentropic expansion while work is done until V5 = V1
5-1 Constant-volume heat rejection to the initial state
- (a) Sketch the P-ν and T-s diagrams for this cycle.
- (b) Obtain an expression for the cycle thermal efficiency as a function of k, r, rc, and rp.
- (c) Evaluate the limit of the efficiency as rp approaches unity, and compare your answer with the expression for the Diesel cycle efficiency.
- (d) Evaluate the limit of the efficiency as rc approaches unity, and compare your answer with the expression for the Otto cycle efficiency.
(a)
Draw the
Answer to Problem 64P
The
Explanation of Solution
Draw the
Thus, the
(b)
The expression for the back work ratio as a function of k and r.
Answer to Problem 64P
The expression for the back work ratio as a function of
Explanation of Solution
Apply first law to the closed system for processes 2-3, 3-4, and 5-1 to get the expression of
Here, heat added to the system and heat rejected from the system is
Express the cycle thermal efficiency.
Conclusion:
Process 1-2: Isentropic
Calculate the ratio of
Here, volume at states 1 and 2 is
Process 2-3: Constant volume
Calculate the expression for
Here, pressure at state 1 and 2 is
Process 3-4: Constant pressure
Calculate the expression for
Here, compression ratio is
Process 4-5: Isentropic
Calculate the expression for
Process 5-1: Constant volume
Calculate the expression for
Substitute
Calculate the ratio of
Substitute
Substitute
Substitute
Thus, the expression for the back work ratio as a function of
(c)
The limit of the efficiency as
Answer to Problem 64P
The limit of the efficiency as
Explanation of Solution
Recall the expression for the back work ratio as a function of
Thus, the limit of the efficiency as
The limit of the efficiency as
(d)
The limit of the efficiency as
Answer to Problem 64P
The limit of the efficiency as
Explanation of Solution
Recall the expression for the back work ratio as a function of
Thus, the limit of the efficiency as
The limit of the efficiency as
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Chapter 9 Solutions
Thermodynamics: An Engineering Approach
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