An ideal gas is enclosed in a cylinder at a p | vedclass

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

Question

(B) The mean time between two successive collisions is given by $	au = \frac{\lambda}{v_{avg}}$,where $\lambda$ is the mean free path and $v_{avg}$ i

Vedclass · Accepted Answer

$4 	imes 10^{-8} \, s$

Vedclass · Answer

(B) The mean time between two successive collisions is given by $	au = \frac{\lambda}{v_{avg}}$,where $\lambda$ is the mean free path and $v_{avg}$ is the average speed.Since $\lambda \propto \frac{T}{P}$ and $v_{avg} \propto \sqrt{T}$,we have $	au \propto \frac{T/P}{\sqrt{T}} \propto \frac{\sqrt{T}}{P}$.Given $P_1 = 2 \, atm$,$T_1 = 300 \, K$,and $	au_1 = 6 	imes 10^{-8} \, s$.For the new state,$P_2 = 2 P_1 = 4 \, atm$ and $T_2 = 500 \, K$.Using the ratio $\frac{	au_2}{	au_1} = \frac{P_1}{P_2} \sqrt{\frac{T_2}{T_1}}$:$\frac{	au_2}{6 	imes 10^{-8}} = \frac{2}{4} \sqrt{\frac{500}{300}} = \frac{1}{2} \sqrt{\frac{5}{3}}$.$	au_2 = 6 	imes 10^{-8} 	imes 0.5 	imes 1.29 \approx 3.87 	imes 10^{-8} \, s$.This is closest to $4 	imes 10^{-8} \, s$.

Similar Questions

An ideal gas $A$ and a real gas $B$ have their volumes increased from $V$ to $2V$ under isothermal conditions. The increase in internal energy
[$AIPMT$ $1993$]

The mean free path for a gas,with molecular diameter $d$ and number density $n$,can be expressed as:

Consider an ideal gas at pressure $p$, volume $V$ and temperature $T$. The mean free path for molecules of the gas is $L$. If the radius of gas molecules, as well as pressure, volume and temperature of the gas are doubled, then the mean free path will be

$A$ $25 \times 10^{-3} \, m^3$ volume cylinder is filled with $1 \, mol$ of $O_2$ gas at room temperature $(300 \, K)$. The molecular diameter of $O_2$ is $0.3 \, nm$ and its root mean square speed is $200 \, m/s$. What is the average collision rate (per second) for an $O_2$ molecule?

For a van der Waals gas,if $P_c, V_c$,and $T_c$ are the critical pressure,volume,and temperature respectively,then the value of $P_cV_c/T_c$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module