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Q.

Gas at a pressure P₀ in contained as a vessel. If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure P will be equal to:

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a

2P₀

b

4P₀

c

P₀

d

P₀/ 2

answer is B.

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Detailed Solution

$P = \frac{1}{3} \frac{m N}{V} v_{r m s}^{2} ∴ P \propto m v_{r m s}^{2} S o, \frac{P_{2}}{P_{1}} = \frac{m_{2}}{m'_{}} \times {(\frac{v_{2}}{v_{1}})}^{2} = \frac{m_{1} / 2}{m_{1}} {(\frac{2 v_{1}}{v_{1}})}^{2} = 2 \Rightarrow P_{2} = 2 P_{1} = 2 P_{0}$

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