1 text{ mole} of ideal monoatomic gas (gamma_ | vedclass

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(A) For a monoatomic gas,$C_{v1} = \frac{R}{\gamma_1 - 1} = \frac{R}{5/3 - 1} = \frac{3R}{2}$ and $C_{p1} = \gamma_1 C_{v1} = \frac{5}{3} 	imes \frac

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$3/2$

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(A) For a monoatomic gas,$C_{v1} = \frac{R}{\gamma_1 - 1} = \frac{R}{5/3 - 1} = \frac{3R}{2}$ and $C_{p1} = \gamma_1 C_{v1} = \frac{5}{3} 	imes \frac{3R}{2} = \frac{5R}{2}$.For a diatomic gas,$C_{v2} = \frac{R}{\gamma_2 - 1} = \frac{R}{7/5 - 1} = \frac{5R}{2}$ and $C_{p2} = \gamma_2 C_{v2} = \frac{7}{5} 	imes \frac{5R}{2} = \frac{7R}{2}$.For the mixture,the total heat capacity at constant volume is $C_{v, 	ext{mix}} = \frac{n_1 C_{v1} + n_2 C_{v2}}{n_1 + n_2} = \frac{1 	imes \frac{3R}{2} + 1 	imes \frac{5R}{2}}{1 + 1} = \frac{4R}{2} = 2R$.The total heat capacity at constant pressure is $C_{p, 	ext{mix}} = \frac{n_1 C_{p1} + n_2 C_{p2}}{n_1 + n_2} = \frac{1 	imes \frac{5R}{2} + 1 	imes \frac{7R}{2}}{1 + 1} = \frac{6R}{2} = 3R$.Thus,$\gamma_{	ext{mix}} = \frac{C_{p, 	ext{mix}}}{C_{v, 	ext{mix}}} = \frac{3R}{2R} = 3/2$.

$1 \text{ mole}$ of ideal monoatomic gas $(\gamma_1 = 5/3)$ is mixed with $1 \text{ mole}$ of diatomic gas $(\gamma_2 = 7/5)$. What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure to that at constant volume.

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