A) 4/3
B) 2
C) 5/3
D) 3/2
Correct Answer: D
Solution :
Key Idea For adidbatic process \[p{{V}^{\gamma }}=\text{constant}\text{.}\] Give that, \[p\propto {{T}^{3}}\] or \[p{{T}^{-3}}=\text{constant}\] ?(i) Also for adiabatic process, \[p{{V}^{\gamma }}=\text{constant}\] but \[pV=RT\] (ideal gas law) or \[V=\frac{RT}{p}\] \[\therefore \] \[p{{\left( \frac{RT}{p} \right)}^{\gamma }}=\text{constant}\] \[{{p}^{1-\gamma }}{{T}^{\gamma }}=\text{constant}\] or \[p{{T}^{\gamma /(1-\gamma )}}=\text{constant}\] ?(ii) Equating Eqs. (i) and (ii), we get \[\frac{\gamma }{1-\gamma }=-3\] or \[\gamma =-3+3\gamma \] or \[2\gamma =3\] or \[\gamma =3/2\] or \[\frac{{{C}_{p}}}{{{C}_{v}}}=3/2\]
You need to login to perform this action.
You will be redirected in
3 sec
