A) 4/3
B) 2
C) 5/3
D) 3/2
Correct Answer: D
Solution :
Key Idea For adiabatic process\[p{{V}^{\gamma }}=\]constant. 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 \[{{p}^{1-\gamma }}{{T}^{\gamma }}=\] 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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