Five gas molecules chosen at random are found | vedclass

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

Question

(B) The average speed $v_{av}$ is calculated as:$v_{av} = \frac{500 + 600 + 700 + 800 + 900}{5} = \frac{3500}{5} = 700 \ m/s$The root mean square spee

Vedclass · Accepted Answer

The root mean square speed is $14 \ m/s$ higher than the average speed.

Vedclass · Answer

(B) The average speed $v_{av}$ is calculated as:$v_{av} = \frac{500 + 600 + 700 + 800 + 900}{5} = \frac{3500}{5} = 700 \ m/s$The root mean square speed $v_{rms}$ is calculated as:$v_{rms} = \sqrt{\frac{500^2 + 600^2 + 700^2 + 800^2 + 900^2}{5}}$$v_{rms} = \sqrt{\frac{250000 + 360000 + 490000 + 640000 + 810000}{5}}$$v_{rms} = \sqrt{\frac{2550000}{5}} = \sqrt{510000} \approx 714.14 \ m/s$Rounding to the nearest integer,$v_{rms} \approx 714 \ m/s$.Thus,the root mean square speed is $714 - 700 = 14 \ m/s$ higher than the average speed.

Five gas molecules chosen at random are found to have speeds of $500, 600, 700, 800$ and $900 \ m/s$. Which of the following statements is correct?

Similar Questions

If $c$ is the $rms$ speed of molecules in a gas and $v$ is the speed of sound waves in the gas,show that $\frac{c}{v}$ is constant and independent of temperature for all diatomic gases.

At a given temperature,the root mean square velocities of oxygen and hydrogen molecules are in the ratio:

At a given temperature,the $rms$ velocity of a gas molecule of mass $m$ is proportional to:

At room temperature,the $rms$ speed of a gas is $V_1$. If the pressure of the gas is doubled at the same room temperature,the $rms$ speed becomes $V_2$. Then:

The $r.m.s.$ speed of the molecules of a gas in a vessel is $400 \; m/s$. If half of the gas leaks out,at constant temperature,the $r.m.s.$ speed of the remaining molecules will be ..... $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module