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(B) The root mean square (rms) speed of ideal gas particles is given by the formula:$v_{rms} = \sqrt{\frac{3kT}{m}}$This implies that $v_{rms} \propto

Vedclass · Accepted Answer

$927$

Vedclass · Answer

(B) The root mean square (rms) speed of ideal gas particles is given by the formula:$v_{rms} = \sqrt{\frac{3kT}{m}}$This implies that $v_{rms} \propto \sqrt{T}$, where $T$ is the absolute temperature in Kelvin.Therefore, the ratio of the rms speeds is:$\frac{v_{1,rms}}{v_{2,rms}} = \sqrt{\frac{T_1}{T_2}}$Given that the final rms speed is $2$ times the initial rms speed, $v_{2,rms} = 2v_{1,rms}$.The initial temperature $T_1 = 27^{\circ} C = 27 + 273 = 300 \ K$.Substituting these values into the ratio:$\frac{v_{1,rms}}{2v_{1,rms}} = \sqrt{\frac{300}{T_2}}$$\frac{1}{2} = \sqrt{\frac{300}{T_2}}$Squaring both sides:$\frac{1}{4} = \frac{300}{T_2}$$T_2 = 1200 \ K$To convert the final temperature back to Celsius:$T_2(^{\circ} C) = 1200 - 273 = 927^{\circ} C$.Thus, the correct option is $B$.

An ideal gas in a closed container is heated so that the final rms speed of the gas particles increases by $2$ times the initial rms speed. If the initial gas temperature is $27^{\circ} C$, then the final temperature of the ideal gas is : (in $^{\circ} C$)

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