Question

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 ?

• A. $-123^{\circ} C$
• B. $123^{\circ} C$
• C. $-100^{\circ} C$
• D. $0^{\circ} C$

Answer 1

Answer: (A)

$-123^{\circ} C$

Answer 2

$v_{ rms } \propto \sqrt{\frac{3 R T}{M}}$ $\Rightarrow T \propto v_{ rms }^{2}$ $\Rightarrow \frac{T_{2}}{T_{1}}=\left[\frac{v_{2}}{v_{1}}\right]^{2}$ $=\frac{1}{4}$ $\Rightarrow T_{2}=\frac{T_{1}}{4}=\frac{(273+327)}{4}$ $=150 K =-123^{\circ} C$