If three moles of monoatomic gas (γ = 5/3) is mixed with two moles of a diatomic gas (γ = 7/5), the value of adiabatic exponent γ for the mixture is (a) 1.35 (b) 1.52 (c) 1.40 (d) 1.75

Answer: (b). CVmix = (3 × 3/2R + 2 × 5/2R)/(5) = 9.5R/5 = 1.9R CPmix = CVmix + R = 2.9R γ = (2.9)/(1.9) ≈ 1.52 So the answer is (b) 1.52.

If three moles of monoatomic gas (γ = 5/3) is mixed with two moles of… | JEE Main 2024 (30 Jan, Shift 2)

Q20JEE Main 2024 · 30 JAN · SHIFT 2Medium

Specific Heats of Gases - Cp, Cv, γ & Mayer's Relation

If three moles of monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is mixed with two moles of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ , the value of adiabatic exponent $\gamma$ for the mixture is

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Answer: (b)

$C_V^{mix} = \dfrac{3 \times \frac{3}{2}R + 2 \times \frac{5}{2}R}{5} = \dfrac{9.5R}{5} = 1.9R$
$C_P^{mix} = C_V^{mix} + R = 2.9R$
$\gamma = \dfrac{2.9}{1.9} \approx 1.52$
So the answer is (b) 1.52.

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Specific Heats of Gases - Cp, Cv, γ & Mayer's Relation question from JEE Main 2024 (30 Jan, Shift 2)

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