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Answer: What is the thermal efficiency of an engine that
Chapter 20, Problem 46P(choose chapter or problem)
Problem 46P
What is the thermal efficiency of an engine that operates by taking n moles of diatomic ideal gas through the cycle \(1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 1\) shown in Fig. P20.46?
Equation Transcription:
Text Transcription:
1-2-3-4-1
2p_0
p_0
v_0
2V_0
Questions & Answers
QUESTION:
Problem 46P
What is the thermal efficiency of an engine that operates by taking n moles of diatomic ideal gas through the cycle \(1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 1\) shown in Fig. P20.46?
Equation Transcription:
Text Transcription:
1-2-3-4-1
2p_0
p_0
v_0
2V_0
ANSWER:
Solution 46P
Step 1:
The process, 1 ➝ 2 is an isochoric process. Therefore, the work done by the system will be zero.
According to ideal gas equation, at point 1,
P1V1 = nRT1
Where, “n” is the number of moles of the gas
P1 - Pressure at point 1
V1 - Volume at point 1
R - Universal gas constant
T1 - Temperature at point 1
T1 = P1V1/nR
From the graph, we can see that, P1 = P0 and V1 = V0
Therefore, T1 = P0V0/nR
Similarly, T2 = 2P0V0/nR
The heat change in the system, Q = nCVΔT
Where, CV - Specific heat capacity at constant volume
ΔT - Change in temperature of the system
In process 1 ➝ 2, ΔT = T2 - T1 = 2P0V0/nR - P0V0/nR = P0V0/nR
For a diatomic gas, CV = 5/2 R
Therefore, Q = n×(5/2)R×P0V0/nR = 5P0V0 / 2