Question

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

• A. 1.4
• B. 1.5
• C. 1.53
• D. 3.07

Answer 1

Answer: (C)

1.53

Answer 2

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 g is the weighted mean of $\gamma_1$ and $\gamma_2$ i.e., $\gamma = \frac{n_{1}\gamma_{1} + n_{2} \gamma_{2}}{n_{1} + n_{2}} = \frac{ 1\left(5/3\right) + 1 \left(7/5\right)}{1+1}$ $= \frac{25 + 21 }{15 \times2} = \frac{46}{30} = 1.53$