The temperature of an ideal gas is increased | vedclass

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(A) The root mean square (r.m.s.) speed of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this relation,we can see that $

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twice.

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(A) The root mean square (r.m.s.) speed of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this relation,we can see that $v_{rms} \propto \sqrt{T}$.Given initial temperature $T_1 = 27^{\circ} C = 27 + 273 = 300 \ K$.Given final temperature $T_2 = 927^{\circ} C = 927 + 273 = 1200 \ K$.Taking the ratio of the speeds:$\frac{v_{rms_2}}{v_{rms_1}} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{1200}{300}} = \sqrt{4} = 2$.Therefore,$v_{rms_2} = 2 \cdot v_{rms_1}$.The r.m.s. speed becomes twice the initial speed.

The temperature of an ideal gas is increased from $27^{\circ} C$ to $927^{\circ} C$. The r.m.s. speed of its molecules becomes

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