The rms speed of an ideal hydrogen gas molecu | vedclass

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(D) The formula for the $rms$ speed of a gas is given by $v_{rms} = \sqrt{\frac{3P}{ho}}$.Given: $v_{rms} = 3180 \ m/s$,$ho = 8.99 	imes 10^{-2}

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(D) The formula for the $rms$ speed of a gas is given by $v_{rms} = \sqrt{\frac{3P}{ho}}$.Given: $v_{rms} = 3180 \ m/s$,$ho = 8.99 	imes 10^{-2} \ kg/m^3$.Squaring both sides,we get $v_{rms}^2 = \frac{3P}{ho}$.Rearranging for pressure $P$: $P = \frac{v_{rms}^2 	imes ho}{3}$.Substituting the values: $P = \frac{(3180)^2 	imes 8.99 	imes 10^{-2}}{3}$.$P = \frac{10112400 	imes 0.0899}{3} \approx \frac{909104.76}{3} \approx 303034.92 \ N/m^2$.To convert to atmospheres: $P_{atm} = \frac{303034.92}{1.01 	imes 10^5} \approx \frac{303034.92}{101000} \approx 3.0 \ atm$.

The $rms$ speed of an ideal hydrogen gas molecule in a gas chamber at $0^{\circ}C$ is $3180 \ m/s$. What is the pressure of the hydrogen gas in atmospheres? (Given: Density of hydrogen gas $\rho = 8.99 \times 10^{-2} \ kg/m^3$,$1 \ atm = 1.01 \times 10^5 \ N/m^2$)

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