If one mole of a monoatomic gas (γ = 5/3) is mixed with one mole of a diatomic gas…

Q: If one mole of a monoatomic gas (γ = 5/3) is mixed with one mole of a diatomic gas (γ = 7/5), the value of γ for the mixture is

(a) 1.40

(b) 1.50

(c) 1.53

(d) 3.07

Ans: (b)

Sol: For monoatomic gas $\large C_{V_1} = \frac{3}{2}R $

For diatomic gas $\large C_{V_2} = \frac{5}{2}R $

For mixture $\large C_V = \frac{n_1 C_{V_1} + n_2 C_{V_2} }{n_1 + n_2}$

$\large C_V = \frac{1 \times \frac{3}{2}R + 1 \times \frac{5}{2}R }{1 + 1} = 2R $

$\large C_P – C_V = R $

$\large C_P = 2R + R = 3 R$

$\large \gamma_{mixture} = \frac{C_P}{C_V} = \frac{3R}{2R}$

= 1.5