JEE Main 2022 · Physics · Thermodynamics and Kinetic Theory of Gases · medium

A mixture of 2 moles of helium (monatomic) and 1 mole of oxygen (rigid diatomic) behaves as an ideal gas. The ratio of its specific heats is γ=17/N.…

Numerical answer

A mixture of

2

moles of helium (monatomic) and

1

mole of oxygen (rigid diatomic) behaves as an ideal gas. The ratio of its specific heats is

\gamma=\dfrac{17}{N}

. The integer

N

Show answer and solution

Answer: 11

For a mixture, the total heat capacities add:

nC_v=\sum n_iC_{v,i}

. Here

C_{v}^{mix}=\dfrac{2\left(\frac32R\right)+1\left(\frac52R\right)}{3}=\dfrac{5.5R}{3}=\dfrac{11R}{6}

. Then

C_p^{mix}=C_v+R=\dfrac{17R}{6}

. Hence

\gamma=\dfrac{C_p}{C_v}=\dfrac{17}{11}\approx1.55

, which lies between

\frac53

and

\frac75

as it must. So

N=11

. Averaging the two

\gamma

values directly would be wrong.

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