The temperature of an ideal gas is increased | vedclass

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(A) The root mean square speed $(v_{rms})$ of an ideal gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.This implies that $v_{rms} \propto

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(A) The root mean square speed $(v_{rms})$ of an ideal gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.This implies that $v_{rms} \propto \sqrt{T}$,where $T$ is the absolute temperature in Kelvin.Initial temperature $T_1 = 27^{\circ}C = 27 + 273 = 300 \ K$.Final temperature $T_2 = 927^{\circ}C = 927 + 273 = 1200 \ K$.Using the ratio: $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$.Substituting the values: $\frac{v_2}{v_1} = \sqrt{\frac{1200}{300}} = \sqrt{4} = 2$.Therefore,$v_2 = 2v_1$. The root mean square speed becomes twice the initial speed.

The temperature of an ideal gas is increased from $27^{\circ}C$ to $927^{\circ}C$. The root mean square speed of its molecules becomes:

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