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:
$P \propto T^{3} \Rightarrow PT^{-3}=$ constan
$PV^{\gamma}=$ const
$P\left(\frac{nRT}{P}\right)^{\gamma}=$ const
$P^{1-\gamma} T^{\gamma}=$ const
$PT^{\frac{\gamma}{1-\gamma}}=$ const
$\frac{\gamma}{1-\gamma}=-3$
$\gamma=-3+3 \gamma$
$3=2 \gamma$
$\gamma=\frac{3}{2}$
