A) \[\gamma R\]
B) \[\frac{(\gamma -1)R}{\gamma }\]
C) \[\frac{R}{\gamma -1}\]
D) \[\frac{\gamma R}{\gamma -1}\]
Correct Answer: C
Solution :
From the Mayer?s formula \[{{C}_{P}}-{{C}_{V}}=R\] ... (i) and \[\gamma =\frac{{{C}_{P}}}{{{C}_{V}}}\] \[\Rightarrow \] \[\gamma {{C}_{V}}={{C}_{P}}\] ... (ii) Substituting Eq. (ii) in Eq. (i), we get \[\gamma {{C}_{V}}-{{V}_{V}}=R\] \[{{C}_{V}}(\gamma -1)=R\] \[{{C}_{V}}=\frac{R}{\gamma -1}\]
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