At a temperature of 27^{circ}C and a pressure | vedclass

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(C) The $rms$ speed of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this,we can see that $v_{rms} \propto \sqrt{T}$.Note that t

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$\frac{400}{\sqrt{3}} \, m/s$

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(C) The $rms$ speed of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this,we can see that $v_{rms} \propto \sqrt{T}$.Note that the $rms$ speed is independent of the pressure of the gas.Given: $T_1 = 27^{\circ}C = 27 + 273 = 300 \, K$ and $v_1 = 200 \, m/s$.Given: $T_2 = 127^{\circ}C = 127 + 273 = 400 \, K$.Using the proportionality $v_1 / v_2 = \sqrt{T_1 / T_2}$:$\frac{200}{v_2} = \sqrt{\frac{300}{400}} = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}$.Therefore,$v_2 = \frac{200 	imes 2}{\sqrt{3}} = \frac{400}{\sqrt{3}} \, m/s$.

At a temperature of $27^{\circ}C$ and a pressure of $1.0 \times 10^5 \, N/m^2$,the $rms$ speed of a gas is $200 \, m/s$. What is the $rms$ speed at a temperature of $127^{\circ}C$ and a pressure of $0.5 \times 10^5 \, N/m^2$?

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