A) \[\frac{5}{4}\]
B) \[\frac{5}{3}\]
C) \[\frac{5}{2}\]
D) \[\frac{3}{5}\]
Correct Answer: C
Solution :
Key Idea: Poissons equation for adiabatic process is given by \[P{{V}^{\gamma }}=constant.\] For adiabatic process, Poissons equation is given by \[P{{V}^{\gamma }}=constant.\] ?....(1) Ideal gas relation is \[PV=RT\] \[\Rightarrow \] \[V=\frac{RT}{P}\] ?...(2) From Eqs. (1) and (2), we get \[P{{\left( \frac{RT}{P} \right)}^{\gamma }}=constant\] \[\Rightarrow \] \[\frac{{{\text{T}}^{}}}{{{\text{P}}^{\text{-1}}}}\text{=constant}\] ?....(3) where \[\gamma \] is ratio of specific heats of the gas. Given, \[p\,\alpha \,{{T}^{C}}\] ?...(4) On comparing with Eq. (3), we have \[C=\frac{\gamma }{\gamma -1}\] For a monoatomic gas \[\gamma =\frac{5}{3}\] \[\therefore \] We have \[C=\frac{\frac{5}{3}}{\frac{5}{3}-1}=\frac{5}{2}\]
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