Question

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

• A. 1.4
• B. 1.5
• C. 1.53
• D. 3.07

Answer 1

Answer: (B)

1.5

Answer 2

$\gamma_1 =\frac{5}{3}$ means gas is monoatomic or $C_v{_1}=\frac{3}{2}R$
$\gamma_2=\frac{7}{5}$ means gas is diatomic or $C_v{_2}=\frac{5}{2}R$
C$_v$ (of the mixture)
$=\frac{n_1C_v{_1}+n_2C_v{_2}}{n_1+n_2}=\frac{(1)\bigg(\frac{3}{2}R\bigg)+(1)\bigg(\frac{5}{2}R\bigg)}{1+1}=2R$
$C_p$ (of the mixture) $=C_v+R=3R$
$\therefore \, \, \, \gamma_{mixture}=\frac{C_p}{C_v}=\frac{3R}{2R}=1.5$
$\therefore \, \,$ Correct option is (b).