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

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Heat & Thermodynamics

If three moles of monoatomic gas

(γ = \frac{5}{3})

is mixed with two moles of a diatomic gas

(γ = \frac{7}{5})

, the value of adiabatic exponent

γ

for the mixture is:

(A)1.75
(B)1.40
(C)1.52✓ Correct
(D)1.35

Answer: (C)

Solution

For a mixture of gases, the effective degrees of freedom is the mole-weighted average:

f_{mi x} = \frac{n _{1} f _{1} + n _{2} f _{2}}{n _{1} + n _{2}}

For the monoatomic gas,

f_{1} = 3

n_{1} = 3

; for the diatomic gas,

f_{2} = 5

n_{2} = 2

f_{mi x} = \frac{3 ( 3 ) + 2 ( 5 )}{3 + 2} = \frac{9 + 10}{5} = \frac{19}{5}

The adiabatic exponent is

γ_{mi x} = 1 + \frac{2}{f _{mi x}} = 1 + \frac{2 \times 5}{19} = 1 + \frac{10}{19} = \frac{29}{19} \approx 1.52

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Single correct option

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