The temperature should the hydrogen at 327 ° C be cooled at constant pressure so that the root mean square velocity of its molecules becomes half of its previous value is

Question

The temperature should the hydrogen at 327 ° C be cooled at constant pressure so that the root mean square velocity of its molecules becomes half of its previous value is (A) -123° C (B) 123 ° C (C) -100 ° C (D) 0° C

Tardigrade Admin · Accepted Answer

vr m s propto √(3 R T/M) ⇒ T propto vr m s2 ⇒ (T2/T1)=[(v2/v1)]2=(1/4) ⇒ T2=(T1/4)=(273 + 327/4) =150 K=-123â

Q. The 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 is

$- 12 3^{\circ} C$

$123^{\circ} C$

$- 100^{\circ} C$

$0^{\circ} C$

$v_{r m s} \propto \frac{3 RT}{M}$
$\Rightarrow T \propto v_{r m s}^{2}$
$\Rightarrow \frac{T _{2}}{T _{1}} = [\frac{v _{2}}{v _{1}}]^{2} = \frac{1}{4} \Rightarrow T_{2} = \frac{T _{1}}{4} = \frac{273 + 327}{4}$
$= 150 K = - 123℃$

Q. The temperature should the hydrogen at 327∘C be cooled at constant pressure so that the root mean square velocity of its molecules becomes half of its previous value is

−123∘C

123∘C

−100∘C

0∘C