The root mean square speed of molecules of ni | vedclass

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

Question

(A) The root mean square speed $(V_{rms})$ of gas molecules is given by the formula: $V_{rms} = \sqrt{\frac{3 k_{B} T}{m}}$.Given:Temperature $T = 27^

Vedclass · Accepted Answer

$523$

Vedclass · Answer

(A) The root mean square speed $(V_{rms})$ of gas molecules is given by the formula: $V_{rms} = \sqrt{\frac{3 k_{B} T}{m}}$.Given:Temperature $T = 27^{\circ} C = 27 + 273 = 300 \, K$.Mass of a nitrogen molecule $m = 4.6 	imes 10^{-26} \, kg$.Boltzmann constant $k_{B} = 1.4 	imes 10^{-23} \, J K^{-1}$.Substituting the values into the formula:$V_{rms} = \sqrt{\frac{3 	imes 1.4 	imes 10^{-23} 	imes 300}{4.6 	imes 10^{-26}}}$$V_{rms} = \sqrt{\frac{1260 	imes 10^{-23}}{4.6 	imes 10^{-26}}}$$V_{rms} = \sqrt{273.91 	imes 10^{3}} \approx \sqrt{273910} \approx 523.36 \, m/s$.Thus,the approximate speed is $523 \, m/s$.

The root mean square speed of molecules of nitrogen gas at $27^{\circ} C$ is approximately $.......m/s$. (Given: mass of a nitrogen molecule $= 4.6 \times 10^{-26} \, kg$ and Boltzmann constant $k_{B} = 1.4 \times 10^{-23} \, J K^{-1}$)

Similar Questions

If at $STP$,the velocity of sound in a gas $(\gamma = 1.5)$ is $600 \, m/s$,the $r.m.s.$ velocity of the gas molecules at $STP$ will be ........... $m/s$.

If the pressure of a gas is doubled while keeping the temperature constant,what will happen to the root mean square $(RMS)$ speed of the gas molecules?

If $V_{rms}$ for $O_2$ molecules is $V$ at temperature $T \ K$. Then $V_{rms}$ for oxygen atoms at temperature $2T$ will be

If the $rms$ speed of hydrogen gas is equal to the $rms$ speed of oxygen gas at $47^{\circ}C$,find the temperature of the hydrogen gas in $K$.

At a given temperature,which gas has a higher speed: light or heavy?

Vedclass Test Series

Exam Paper Generator

Online Exam Module