Q 11-12-124JEE MainJEE Main 2020 (7 Jan, Shift 1)Medium
Two moles of an ideal gas with $\dfrac{C_P}{C_V} = \dfrac53$ are mixed with three moles of another ideal gas with $\dfrac{C_P}{C_V} = \dfrac43$. The value of $\dfrac{C_P}{C_V}$ for the mixture is:
Answer: (D) $1.42$
$C_V = \dfrac{R}{\gamma - 1}$: for the first gas $C_V = \tfrac32R$, for the second $C_V = 3R$.
$$C_V^{\text{mix}} = \frac{2\times\frac32R + 3\times3R}{5} = \frac{12}{5}R, \qquad C_P^{\text{mix}} = C_V^{\text{mix}} + R = \frac{17}{5}R$$
$$\gamma_{\text{mix}} = \frac{17}{12} \approx 1.42$$
Solution by Sreeraj P, M.Sc Physics