The root mean square velocity of an ideal gas | vedclass

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(B) The root mean square velocity $(U_{rms})$ is given by the formula $U_{rms} = \sqrt{\frac{3RT}{M}}$.Since $U_{rms} \propto \sqrt{T}$,we have $\frac

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By heating the gas,the pressure is quadrupled (i.e.,made four times)

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(B) The root mean square velocity $(U_{rms})$ is given by the formula $U_{rms} = \sqrt{\frac{3RT}{M}}$.Since $U_{rms} \propto \sqrt{T}$,we have $\frac{U_1}{U_2} = \sqrt{\frac{T_1}{T_2}}$.Given $U_1 = 5 	imes 10^4 \ cm \ s^{-1}$ and $U_2 = 10 	imes 10^4 \ cm \ s^{-1}$,then $\frac{U_1}{U_2} = \frac{1}{2}$.Squaring both sides,$\frac{T_1}{T_2} = (\frac{1}{2})^2 = \frac{1}{4}$,which means $T_2 = 4T_1$.For an ideal gas in a fixed volume,$P \propto T$ (Gay-Lussac's Law). Since the temperature is quadrupled,the pressure also becomes four times the initial value.

The root mean square velocity of an ideal gas in a closed container of fixed volume is increased from $5 \times 10^4 \ cm \ s^{-1}$ to $10 \times 10^4 \ cm \ s^{-1}$. Which of the following statements correctly explains how the change is accomplished?

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