Question

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

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

Answer 1

Answer: (B)

$1.50$

For monoatomic gas :

$C_v=\frac{3}{2}R$

$C_p=\frac{5}{2}R$
For diatomic gas :

$C_v=\frac{5}{2}R$

$C_p=\frac{7}{2}R$
For mixture of 1 mole of each :

$C_v=\frac{\frac{3}{2}R+\frac{5}{2}R}{2}=2R$

$C_p=\frac{\frac{5}{2}R+\frac{7}{2}R}{2}=3R$

$\gamma =\frac{C_p}{C_v}$

$\gamma =\frac{3R}{2R}$

$\gamma =1.50$

Hence, the correct option is B.