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To what temperature should the hydrogen at $327^{0} C$ be cooled at constant pressure, so that the root mean square velocity of its molecules becomes half of its previous value.

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$- 123^{0} C$

$23^{0} C$

$- 100^{0} C$

$0^{0} C$

answer is A.

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Detailed Solution

For hydrogen (M=2gm)

Case(i)

$T_{1} = 600 K; V_{1} = \sqrt{\frac{3 {RT}_{1}}{M}}$

Case(ii)

$T_{2} = ?; V_{1} = \sqrt{\frac{3 {RT}_{1}}{M}}$

$Given, V_{2} = \frac{V_{1}}{2} \Rightarrow \sqrt{\frac{3 {RT}_{2}}{M}} = \frac{1}{2} (\sqrt{\frac{3 {RT}_{1}}{M}})$

$\Rightarrow T_{2} = \frac{1}{4} (T_{1}) = 150 K$

$\Rightarrow T_{2} = - 123 {}^{0}C$

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