Two moles of helium are mixed with n moles of hydrogen. If C _ p C _ v = (3)/(2) for the mixture then the value of n is,

Correct answer: C. 2 γ _ mix = 1 + 2 f _ mix C _ p C _ v = f _ mix + 2 f _ mix = (3)/(2) ⇒ f _ mix = 4 f _ mix = n _ 1 f _ 1 + n _ f _ 2 n _ 1 + n _ 2 ⇒ 4 = (2 × 3 + n × 5)/(2 + n) ⇒ n = 2mole

JEE Main 201816 AprilOnline

Exam: JEE Main
Year: 2018
Date: 16 April
Mode: Online
Subject: Physics
Chapter: Kinetic Theory of Gases

JEE Main 2018 · 16 April · Online · Physics · Kinetic Theory of Gases

Two moles of helium are mixed with n moles of hydrogen. If C _ p C...

Two moles of helium are mixed with n moles of hydrogen. If

\dfrac{{C}_{p}}{{C}_{v}} = \dfrac{3}{2}

for the mixture then the value of

n

is,

Options

A1
B3
C2
D $\dfrac{3}{2}$

Correct answer

C. 2

Step-by-step solution

{\gamma}_{mix} = 1 + \dfrac{2}{{f}_{mix}}

\dfrac{{C}_{p}}{{C}_{v}} = \dfrac{{f}_{mix} + 2}{{f}_{mix}} = \dfrac{3}{2}

⇒ {f}_{mix} = 4

{f}_{mix} = \dfrac{{n}_{1}{f}_{1} + {n}_{}{f}_{2}}{{n}_{1} + {n}_{2}}

⇒ 4 = \dfrac{2 \times 3 + n \times 5}{2 + n}

⇒ n = 2mole

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