At which temperature will the velocity of O_2 | vedclass

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

Question

(C) The root mean square velocity is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since the velocities are equal, we have $\sqrt{\frac{3RT_{

Vedclass · Accepted Answer

$39$

Vedclass · Answer

(C) The root mean square velocity is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since the velocities are equal, we have $\sqrt{\frac{3RT_{O_2}}{M_{O_2}}} = \sqrt{\frac{3RT_{N_2}}{M_{N_2}}}$.Squaring both sides and simplifying, we get $\frac{T_{O_2}}{M_{O_2}} = \frac{T_{N_2}}{M_{N_2}}$, which implies $T_{O_2} = T_{N_2} 	imes \frac{M_{O_2}}{M_{N_2}}$.Given $T_{N_2} = 0 + 273 = 273\,K$, $M_{O_2} = 32\,g/mol$, and $M_{N_2} = 28\,g/mol$.Substituting the values: $T_{O_2} = 273 	imes \frac{32}{28} = 273 	imes \frac{8}{7} = 39 	imes 8 = 312\,K$.Converting back to Celsius: $312 - 273 = 39\,^\circ C$.

At which temperature will the velocity of $O_2$ molecules be equal to the velocity of $N_2$ molecules at $0 ^\circ C$?

Similar Questions

$A$ certain amount of an ideal gas is taken from its initial state $1$ to final state $4$ through the path $1 \rightarrow 2 \rightarrow 3 \rightarrow 4$ as shown in the figure. $AB, CD, EF$ are all isotherms. If $v_p$ is the most probable speed of the molecules, then:

The velocities of $4$ gas molecules are given by $1 \ km/s, 3 \ km/s, 5 \ km/s$ and $7 \ km/s$. Calculate the difference between the average velocity and the root mean square $(RMS)$ velocity. (in $km/s$)

The given diagram shows isotherms for a fixed mass of an ideal gas at temperatures $T_1$ and $T_2$. What is the value of the ratio $\frac{\text{r.m.s. speed of the molecules at temperature } T_2}{\text{r.m.s. speed of the molecules at temperature } T_1}$?

$A$ perfect gas of volume $10 \ L$ is compressed isothermally to a volume of $1 \ L$. The $rms$ speed of the molecules will

Three particles have speeds of $2u$,$10u$,and $11u$. Which of the following statements is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module