A) \[\frac{R}{\left( \gamma -1 \right)}\]
B) \[\frac{\left( \gamma -1 \right)}{R}\]
C) \[\gamma R\]
D) \[\frac{1+\gamma }{1-\gamma }\]
Correct Answer: A
Solution :
[a] \[{{C}_{p}}-{{C}_{v}}=R\Rightarrow {{C}_{p}}={{C}_{v}}+R\] \[\because \,\,\,\,\gamma =\frac{{{C}_{p}}}{{{C}_{v}}}=\frac{{{C}_{v}}+R}{{{C}_{p}}}=\frac{{{C}_{v}}}{{{C}_{v}}}+\frac{R}{{{C}_{v}}}\] \[\Rightarrow \gamma =1+\frac{R}{{{C}_{v}}}\Rightarrow \frac{R}{{{C}_{v}}}=\gamma -1\Rightarrow {{C}_{v}}\] \[=\frac{R}{\gamma -1}\]You need to login to perform this action.
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