JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Heat & Thermodynamics

The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy

2 \times 1 0^{- 9} J

per molecule is:

(A) $0.75 \times 1 0^{11}$
(B) $3 \times 1 0^{11}$
(C) $6 \times 1 0^{11}$
(D) $1.5 \times 1 0^{11}$ ✓ Correct

Answer: (D)

Solution

The mean kinetic energy per molecule is

\frac{3}{2} k T = 2 \times 1 0^{- 9}

J, giving

k T = \frac{4 \times 1 0 ^{- 9}}{3}

. The number of molecules is

N = \frac{P V}{k T}

. With

P = 2 \times 1.013 \times 1 0^{5}

N/m² and

V = 1 0^{- 3}

m³, we get

N = \frac{2 \times 1.013 \times 1 0 ^{5} \times 1 0 ^{- 3}}{\frac{4}{3} \times 1 0 ^{- 9}} \approx 1.5 \times 1 0^{11}

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Single correct option

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