JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Heat & Thermodynamics

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature

2 7^{\circ} C

. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take

R = 8.3 J / K

mole]

(A)0.9 kJ
(B)6 kJ
(C)10 kJ✓ Correct
(D)14 kJ

Answer: (C)

Solution

Since

v_{rms} \propto T

, doubling it needs four times the absolute temperature:

T_{f} = 4 T_{i} = 4 (300) = 1200 K

, a rise of

Δ T = 900 K

. For

15 g

N_{2}

(

M = 28

) that is

n = \frac{15}{28} \approx 0.54 mol

. Nitrogen is diatomic with

f = 5

, so at constant volume

Δ Q = \frac{f}{2} n R Δ T = \frac{5}{2} (0.54) (8.3) (900) \approx 1.0 \times 1 0^{4} J

, about

10 kJ

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Single correct option

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