A) \[\frac{5}{2}\]
B) \[\frac{2}{5}\]
C) \[\frac{5}{3}\]
D) \[\frac{3}{5}\]
Correct Answer: A
Solution :
For adiabatic change \[{{p}^{1-\gamma }}\,{{T}^{\gamma }}=cons\tan t\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,p\propto \,{{T}^{\frac{-\gamma }{1-\gamma }}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,p\propto \,{{T}^{\frac{-\gamma }{\gamma -1}}}\] Value of constant \[k=\frac{\gamma }{\gamma -1}\] \[\gamma =\frac{5}{3}\] for monoatomic gas \[\therefore \,\,\,\,\,\,\,\,\,\,k=\frac{5/3}{5/3-1}\,\,=\,\,\frac{5}{2}\]
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