Question

7 moles of a tetra-atomic non-linear gas $A$ at $10atm$ and $TK$ are mixed with 6 moles of another gas $B$ at $T/3K$ and $5atm$ in a closed, rigid vessel without energy transfer with surroundings. If final temperature of mixture was $5T/6K$, then atomcity of gas $B$ is (Assuming all modes of energy are active)

Answer 1

$C_v$ of gas $A=\frac{3}{2}R+\frac{3}{2}R+6R=9R$
Let $C_v$ of gas $B=X$
Heat lost by gas $A=7\times 9R\times (T-\frac{5T}{6})$
Heat gained by gas $B=6X(\frac{5T}{6}-\frac{T}{3})$
$\Rightarrow 63R(\frac{T}{6})=6X(\frac{T}{2})=X=\frac{7}{2}R$
$\therefore$ gas is diatomic.
and atomcity of gas is 2.