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The density of a gas filled in an electric lamp is $0.75 k g / m^{3} .$ After the lamp has been switched on for sufficient time, the pressure of gas in it increased from $4 \times 10^{4} P a t o 9 \times 10^{4} P a .$ The increase in $u_{r m s}$ of gas molecules is $100 x m s^{- 1}$ . Find the value of ‘x’

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Detailed Solution

Density of gas will remain constant as its mole and volume remains unchanged $Δ u_{r m s} = u_{2} - u_{1} = \sqrt{\frac{3 P_{2}}{d}} - \sqrt{\frac{3 P_{1}}{d}}$

$= \sqrt{\frac{3 \times 9 \times 10^{4}}{0.75}} - \sqrt{\frac{3 \times 4 \times 10^{4}}{0.75}} = 200 m / s$

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