Solution Found!
Solved: (a) For the Otto cycle shown in Fig. 20.6,
Chapter 20, Problem 59P(choose chapter or problem)
Problem 59P
(a) For the Otto cycle shown in Fig. 20.6, calculate the changes in entropy of the gas in each of the constant-volume processes \(b \rightarrow c\) and \(d \rightarrow a\) in terms of the temperatures T_{a}, T_{b}, T_{c}, and \(T_{d}\) and the number of moles n and the heat capacity \(C_{V}\) of the gas. (b) What is the total entropy change in the engine during one cycle? (Hint: Use the relationships between \(T_{a}\) and \(T_{b}\) and between \(T_{d}\) and \(T_{c}\).) (c) The processes \(b \rightarrow c\) and \(d \rightarrow a\) occur irreversibly in a real Otto engine. Explain how can this be reconciled with your result in part (b).
Equation Transcription:
Text Transcription:
b-c
d-a
T_a,T_b,T_c
T-d
C_V
T_a
T_b
T_d
T_c
b-c
d-a
Questions & Answers
QUESTION:
Problem 59P
(a) For the Otto cycle shown in Fig. 20.6, calculate the changes in entropy of the gas in each of the constant-volume processes \(b \rightarrow c\) and \(d \rightarrow a\) in terms of the temperatures T_{a}, T_{b}, T_{c}, and \(T_{d}\) and the number of moles n and the heat capacity \(C_{V}\) of the gas. (b) What is the total entropy change in the engine during one cycle? (Hint: Use the relationships between \(T_{a}\) and \(T_{b}\) and between \(T_{d}\) and \(T_{c}\).) (c) The processes \(b \rightarrow c\) and \(d \rightarrow a\) occur irreversibly in a real Otto engine. Explain how can this be reconciled with your result in part (b).
Equation Transcription:
Text Transcription:
b-c
d-a
T_a,T_b,T_c
T-d
C_V
T_a
T_b
T_d
T_c
b-c
d-a
ANSWER:
Solution 59P
a)
The 1st law of thermodynamics states that,
---------------------(1)
As the volume is unchanged during the processes , the above equation will be reduced to,
----------------------(2)
But we know that,