A) \[{{C}_{V}}=\frac{3}{5}R\]
B) \[{{C}_{P}}=\frac{5}{2}R\]
C) \[{{C}_{P}}-{{C}_{V}}=2R\]
D) \[\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{3}{5}\]
Correct Answer: B
Solution :
Key Idea: Monoatomic gas has three translational degrees of freedom. Specific heat at constant volume \[({{C}_{V}})=\frac{f}{2}R\]and specific heat at constant pressure \[({{C}_{P}})\] \[{{C}_{P}}=\left( \frac{f}{2}+1 \right)R\,\] For monoatomic gas \[f=3\] \[\therefore \] \[{{C}_{V}}=\frac{3}{2}R,{{C}_{P}}=\left( \frac{3}{2}+1 \right)R=\frac{5}{2}R\] From Mayors formula \[{{C}_{P}}-C{{\,}_{V}}\,=R\] \[\therefore \] \[\frac{5}{2}R-\frac{3}{2}R=R\] and \[\gamma =\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{5/2}{3/2}=\frac{5}{3}\]
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