A) 3/5
B) 4/3
C) 5/3
D) 3/2
Correct Answer: D
Solution :
For an adiabatic process the relation between pressure and temperature is given by \[\frac{{{T}^{\gamma }}}{{{P}^{\gamma -1}}}=cons\tan t\] or \[{{T}^{\gamma }}={{p}^{\gamma -1}}\] (Given: \[P\propto {{T}^{3}}\] ) So, \[{{T}^{\gamma }}={{({{T}^{3}})}^{\gamma -1}}\] or \[{{T}^{\gamma }}={{T}^{3\gamma -3}}\] ?(i) Now, equating the power of Eq. (i), we get \[3\gamma -3=\gamma \] So, \[\gamma =\frac{3}{2},\]hence \[\frac{{{C}_{P}}}{{{C}_{V}}}=\gamma =3/2\]
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