A) \[\frac{4}{3}\]
B) \[2\]
C) \[\frac{3}{2}\]
D) \[\frac{3}{2}\]
Correct Answer: D
Solution :
Given that, \[p\propto {{T}^{3}}\] or \[p{{T}^{-3}}=\]constant ... (i) Also for adiabatic process, \[p{{V}^{\gamma }}=\]constant but \[pV=RT\] (ideal gas law) or \[V=\frac{RT}{p}\] \[\therefore \] \[p{{\left( \frac{RT}{p} \right)}^{\gamma }}=\]constant or \[p{{T}^{\gamma (1-\gamma )}}=\]constant ... (ii) Equating Eqs. (i) and (ii), we get \[\frac{\gamma }{1-\gamma }=3\] or \[\gamma =-3+3\gamma \] or \[2\gamma =3\] \[\therefore \] \[\gamma =3/2\] or \[\frac{{{C}_{p}}}{{{C}_{V}}}=3/2\]
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