• # question_answer During an adiabatic process, the pressure of a gas is proportional to the cube of its absolute temperature. The value of$\frac{{{C}_{p}}}{{{C}_{v}}}$for the gas is: A) $\frac{3}{5}$                        B) $\frac{4}{3}$C) $\frac{5}{3}$                        D) $\frac{3}{2}$

$\rho \propto {{T}^{3}}$or $\rho {{T}^{-3}}=k$                                  (1) For adiabatic process $P{{V}^{\gamma }}=C$ or $P{{\left( \frac{RT}{P} \right)}^{\gamma }}=c$or ${{P}^{1-\gamma }}{{T}^{-\gamma }}=C'$ or $P{{T}^{\frac{\gamma }{1-\gamma }}}=C''=k$ Comparing (1) and (2) $\frac{\gamma }{1-\gamma }=-3$or $\gamma =\frac{3}{2}.$ Hence, the correction option is [d].