Thermodynamics Question 4
Question 4 - 2024 (27 Jan Shift 2)
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\frac{C_{p}}{C_{v}}$ for the gas is :
(1) $\frac{5}{3}$
(2) $\frac{3}{2}$
(3) $\frac{7}{5}$
(4) $\frac{9}{7}$
Show Answer
Answer: (2)
Solution:
$\mathrm{P} \propto \mathrm{T}^{3} \Rightarrow \mathrm{PT}^{-3}=$ constan
$\mathrm{PV}^{\gamma}=$ const
$\mathrm{P}\left(\frac{\mathrm{nRT}}{\mathrm{P}}\right)^{\gamma}=$ const
$\mathrm{P}^{1-\gamma} \mathrm{T}^{\gamma}=$ const
$\mathrm{PT}^{\frac{\gamma}{1-\gamma}}=$ const
$\frac{\gamma}{1-\gamma}=-3$
$\gamma=-3+3 \gamma$
$3=2 \gamma$
$\gamma=\frac{3}{2}$
