To what temperature should the hydrogen at 32 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The root mean square velocity $(v_{rms})$ of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $R$ and $M$ are constant

Vedclass · Accepted Answer

$-123$

Vedclass · Answer

(A) The root mean square velocity $(v_{rms})$ of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $R$ and $M$ are constants for a given gas,we have $v_{rms} \propto \sqrt{T}$.This implies $T \propto v_{rms}^2$.Given that the final velocity $v_2$ is half of the initial velocity $v_1$,i.e.,$v_2 = \frac{v_1}{2}$.Therefore,$\frac{T_2}{T_1} = \left(\frac{v_2}{v_1}\right)^2 = \left(\frac{1}{2}\right)^2 = \frac{1}{4}$.The initial temperature $T_1 = 327^{\circ} C = 327 + 273 = 600 \ K$.Thus,$T_2 = \frac{T_1}{4} = \frac{600 \ K}{4} = 150 \ K$.Converting back to Celsius: $T_2 = 150 - 273 = -123^{\circ} C$.

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 $^{\circ} C$)?

Similar Questions

The speeds of $5$ gas molecules are $2, 3, 4, 5,$ and $6$ units respectively. What is the $rms$ speed of these molecules?

One mole of an ideal gas at $STP$ is heated in an insulated closed container until the average speed of its molecules is doubled. Its pressure would therefore increase by what factor?

If the root mean square velocity of the molecules of hydrogen at $NTP$ is $1.84 \, km/s$,calculate the root mean square velocity of oxygen molecule at $NTP$. The molecular weights of hydrogen and oxygen are $2$ and $32$ respectively.

The $r.m.s.$ velocity will be greater for

If the absolute temperature of a gas is increased $5$ times,the r.m.s. velocity of the gas molecules will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module