A) \[\frac{1}{1-\frac{R}{{{c}_{p}}}}\]
B) \[\frac{1}{1-\frac{{{c}_{p}}}{R}}\]
C) \[\frac{1}{1+\frac{{{c}_{p}}}{R}}\]
D) \[\frac{1}{1+\frac{R}{{{c}_{p}}}}\]
Correct Answer: A
Solution :
\[\frac{{{c}_{p}}}{{{c}_{v}}}=\gamma \] and \[{{c}_{p}}-{{c}_{v}}=R\] \[\frac{{{c}_{p}}}{{{c}_{v}}}-1=\frac{R}{{{c}_{v}}}\] \[\frac{{{c}_{p}}}{{{c}_{v}}}=1+\frac{R}{{{c}_{v}}}\] and \[1-\frac{{{c}_{v}}}{{{c}_{p}}}=\frac{R}{{{c}_{p}}}\] \[\frac{{{c}_{v}}}{{{c}_{p}}}=1-\frac{R}{{{c}_{p}}}\] \[\frac{{{c}_{p}}}{{{c}_{v}}}=1-\frac{1}{1-\frac{R}{{{c}_{p}}}}\]
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