To what temperature should the hydrogen at 32 | vedclass

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(A) The root mean square velocity of gas molecules is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $v_{rms} \propto \sqrt{T}$,we have $T \propto v_

Vedclass · Accepted Answer

$-123$

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(A) The root mean square velocity of gas molecules is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $v_{rms} \propto \sqrt{T}$,we have $T \propto v_{rms}^2$.Given that the final velocity $v_2 = \frac{1}{2} v_1$,we can write the ratio as $\frac{T_2}{T_1} = \left(\frac{v_2}{v_1}\right)^2 = \left(\frac{1}{2}\right)^2 = \frac{1}{4}$.The initial temperature $T_1 = 327^{\circ}C = 327 + 273 = 600 K$.Therefore,$T_2 = \frac{T_1}{4} = \frac{600}{4} = 150 K$.Converting the final temperature back to Celsius: $T_2(^{\circ}C) = 150 - 273 = -123^{\circ}C$.

To what temperature should the hydrogen at $327^{\circ}C$ be cooled at constant pressure,so that the root mean square velocity of its molecules becomes half of its previous value? (in $^{\circ}C$)

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