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 curve between absolute temperature $T$ and $v_{rms}^2$ is

$V_{rms}$ denotes the root mean square speed,$\bar{V}$ the average speed,and $V_m$ the most probable speed of gas molecules. Which of the following is the correct relationship?

The $rms$ speeds of the molecules of Hydrogen,Oxygen,and Carbon dioxide at the same temperature are $V_{H}$,$V_{O}$,and $V_{C}$ respectively. Then:

Two containers $A$ and $B$ contain an ideal gas at the same temperature. If the masses of the molecules are $m_A$ and $m_B$ respectively,what is the relationship between their momenta $p_A$ and $p_B$?

The temperature of an ideal gas is increased from $140 \,K$ to $560 \,K$. If the r.m.s. speed of gas molecules is $v$ at $140 \,K$, then at $560 \,K$, the r.m.s. speed becomes:

Vedclass Test Series

Exam Paper Generator

Online Exam Module