One mole of ideal monoatomic gas ($\gamma=5/3$) is mixed with one mole of diatomic gas ($\gamma=7/5$). What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure, to that at constant volume.

JEE Main · 2004 · 24 Apr 2004 · Offline · Heat & Thermodynamics

One mole of ideal monoatomic gas (

γ = 5/3

) is mixed with one mole of diatomic gas (

γ = 7/5

). What is

γ

for the mixture?

γ

denotes the ratio of specific heat at constant pressure, to that at constant volume.

(A) $3/2$ ✓ Correct
(B) $23/15$
(C) $35/23$
(D) $4/3$

Answer: (A)

Solution

For a mixture of ideal gases the molar heat capacities combine as

\frac{n _{1} + n _{2}}{γ _{m} - 1} = \frac{n _{1}}{γ _{1} - 1} + \frac{n _{2}}{γ _{2} - 1}

. With one mole of each and

γ_{1} = \frac{5}{3}

γ_{2} = \frac{7}{5}

, the right-hand side is

\frac{1}{2/3} + \frac{1}{2/5} = \frac{3}{2} + \frac{5}{2} = 4

, so

\frac{2}{γ _{m} - 1} = 4

. That gives

γ_{m} - 1 = \frac{1}{2}

, hence

γ_{m} = \frac{3}{2}

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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