Q 11-12-153JEE MainJEE Main 2018 (16 Apr, Shift 1)Medium
Two moles of helium are mixed with $n$ moles of hydrogen. If $\dfrac{C_p}{C_v} = \dfrac32$ for the mixture then the value of $n$ is,
Answer: (C) $2$
Helium is monatomic ($C_v = \frac32R$, $C_p = \frac52R$) and hydrogen is diatomic ($C_v = \frac52R$, $C_p = \frac72R$). For the mixture,
$$\gamma = \frac{2\cdot\frac52 + n\cdot\frac72}{2\cdot\frac32 + n\cdot\frac52} = \frac{5 + 3.5n}{3 + 2.5n} = \frac32$$
$$10 + 7n = 9 + 7.5n \quad\Rightarrow\quad n = 2$$
Solution by Sreeraj P, M.Sc Physics