JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Heat & Thermodynamics

Consider a mixture of

n

moles of helium gas and

2 n

moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its

C_{P} / C_{V}

value will be

(A) $19/13$ ✓ Correct
(B) $40/27$
(C) $67/45$
(D) $23/15$

Answer: (A)

Solution

For a mixture the ratio of specific heats is

γ_{mix} = \frac{n _{1} C _{p 1} + n _{2} C _{p 2}}{n _{1} C _{v 1} + n _{2} C _{v 2}}

. Helium is monatomic with

C_{v} = \frac{3}{2} R, C_{p} = \frac{5}{2} R

, and oxygen as a rigid diatomic has

C_{v} = \frac{5}{2} R, C_{p} = \frac{7}{2} R

. With

n

moles of helium and

2 n

of oxygen,

γ_{mix} = \frac{n ( \frac{5}{2} R ) + 2 n ( \frac{7}{2} R )}{n ( \frac{3}{2} R ) + 2 n ( \frac{5}{2} R )} = \frac{5 + 14}{3 + 10} = \frac{19}{13}

JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Single correct option

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