Question

If $1$ mole of a monatomic gas $(\gamma =5/3)$ is mixed with $1$ mole of a diatomic gas $(\gamma =7/5)$, the value of $\gamma$ for the mixture is

• A. $1.40$
• B. $1.50$
• C. $1.53$
• D. $3.07$

Answer 1

The correct option is B $1.50$

Let ${\gamma }_1$ and ${\gamma }_2$ denote the ratio of two specific heats of gas 1 and gas 2 respectively when they are mixed in the ratio of $n_1$ and $n_2$ mole. The resultant value of $\gamma$ is the weighted mean of ${\gamma }_1$ and ${\gamma }_2$ i.e.,$\gamma$ = $\frac{n_1{\gamma }_1+n_2{\gamma }_2}{n_1+n_2}$
$=\frac{1\left(5/3\right)+1\left(7/5\right)}{1+1}$
$=\frac{25+21}{15\times 2}$
$=\frac{46}{30}$
$=1.53$