An ideal gas in a container of volume 500 c.c. is at a pressure of 2 × 10⁺⁵ N/m². The average kinetic energy of each molecule is 6 × 10⁻²¹ J. The number of gas molecules in the container is (a) 5 × 10²⁵ (b) 5 × 10²³ (c) 25 × 10²³ (d) 2.5 × 10²²

Answer: (d). PV = 2/3NE, so N = 3PV/2E. V = 500 cc = 5 × 10⁻⁴ m ³ N = 3 × 2 × 10⁵ × 5 × 10⁻⁴2 × 6 × 10⁻²¹ = 3001.2 × 10⁻²⁰ = 2.5 × 10²² So the answer is (d) 2.5 × 10²².

An ideal gas in a container of volume 500 c.c. is at a pressure of 2… | MHT CET 2023 (9 May, Shift 2)

Q26MHT CET 2023 · 9 MAY · SHIFT 2Medium

Pressure & Kinetic Energy of a Gas

An ideal gas in a container of volume 500 c.c. is at a pressure of $2 \times 10^{+5}\text{ N/m}^{2}$ . The average kinetic energy of each molecule is $6 \times 10^{-21}\text{ J}$ . The number of gas molecules in the container is

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Answer: (d)

$PV = \frac{2}{3}N\bar{E}$ , so $N = \frac{3PV}{2\bar{E}}$ .
$V = 500$ cc $= 5 \times 10^{-4}$ m $^3$
$N = \frac{3 \times 2 \times 10^{5} \times 5 \times 10^{-4}}{2 \times 6 \times 10^{-21}} = \frac{300}{1.2 \times 10^{-20}} = 2.5 \times 10^{22}$
So the answer is (d) $2.5 \times 10^{22}$ .

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Pressure & Kinetic Energy of a Gas question from MHT CET 2023 (9 May, Shift 2)

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