JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Heat & Thermodynamics

N moles of a polyatomic gas

(f = 6)

must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is:

(A)6
(B)3
(C)4✓ Correct
(D)2

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}}

Here the polyatomic gas (

f = 6

) has N moles and the monatomic gas (

f = 3

) has 2 moles. For the mixture to behave as a diatomic gas,

f_{mi x} = 5

5 = \frac{N ( 6 ) + 2 ( 3 )}{N + 2}

5 N + 10 = 6 N + 6

N = 4

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Single correct option

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