A) \[\frac{1}{\gamma }\]
B) \[1-\frac{1}{\gamma }\]
C) \[\gamma -1\]
D) \[1-\frac{1}{{{\gamma }^{2}}}\]
Correct Answer: B
Solution :
[b] Fraction of heat supplied used for external work is \[\frac{dW}{dQ}=\frac{dQ-dU}{dQ}=1-\frac{dU}{dQ}\] \[\frac{dW}{dQ}=1-\frac{n{{C}_{v}}\Delta T}{n{{C}_{p}}\Delta T}\] \[\frac{dW}{dQ}=1-\frac{{{C}_{v}}}{{{C}_{p}}}\] \[\frac{{{C}_{v}}}{{{C}_{p}}}=\gamma \] \[\frac{dW}{dQ}=\left[ 1-\frac{1}{\gamma } \right]\]| Note \[dU=n{{C}_{v}}\Delta T\,\,(always)\] \[dQ=n{{C}_{P}}\Delta T\,(at\,cont.p)\] \[dQ=n{{C}_{v}}\Delta T\,(at\,cont.v)\] |
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