At a temperature of 300 K,the average transl | vedclass

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

Question

(D) The average translational kinetic energy $E$ of an ideal gas is given by $E = \frac{3}{2} k_B T$. Thus,$E \propto T$. Given $T_1 = 300 \ K$ and $T

Vedclass · Accepted Answer

$12.42 	imes 10^{-21} \ J, 684 \ m/s$

Vedclass · Answer

(D) The average translational kinetic energy $E$ of an ideal gas is given by $E = \frac{3}{2} k_B T$. Thus,$E \propto T$. Given $T_1 = 300 \ K$ and $T_2 = 600 \ K$,the ratio is $\frac{E_2}{E_1} = \frac{T_2}{T_1} = \frac{600}{300} = 2$. So,$E_2 = 2 	imes E_1 = 2 	imes 6.21 	imes 10^{-21} \ J = 12.42 	imes 10^{-21} \ J$. The $rms$ speed $V_{rms}$ is given by $V_{rms} = \sqrt{\frac{3RT}{M}}$. Thus,$V_{rms} \propto \sqrt{T}$. Given $V_1 = 484 \ m/s$,the new speed $V_2 = V_1 	imes \sqrt{\frac{T_2}{T_1}} = 484 	imes \sqrt{2} \approx 484 	imes 1.414 = 684.37 \ m/s \approx 684 \ m/s$. Therefore,the values are $12.42 	imes 10^{-21} \ J$ and $684 \ m/s$.

At a temperature of $300 \ K$,the average translational kinetic energy and $rms$ speed of a sample of oxygen gas are $6.21 \times 10^{-21} \ J$ and $484 \ m/s$ respectively. At $600 \ K$,these values will be respectively: (Assume ideal gas behavior)

Similar Questions

If $v_1$ is the speed of sound in a diatomic gas at $273^{\circ}C$ and $v_2$ is the r.m.s. speed of its molecules at $273 \ K$,then $\frac{v_1}{v_2}=$

$A$ light container having a diatomic gas enclosed within is moving with velocity $v$. The mass of the gas is $M$ and the number of moles is $n$. The kinetic energy of the gas with respect to the ground is:

If the potential energy of a gas molecule is $U = \frac{M}{r^6} - \frac{N}{r^{12}}$,where $M$ and $N$ are positive constants,then the potential energy at equilibrium must be

During an experiment,an ideal gas is found to obey a condition $\frac{P^2}{\rho} = \text{constant}$ [$\rho = \text{density of the gas}$]. The gas is initially at temperature $T$,pressure $P$,and density $\rho$. The gas expands such that density changes to $\rho/2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module