For a gas at a temperature T,the root-mean-sq | vedclass

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

Question

(B) The expressions for the three speeds of a gas at temperature $T$ are given by:${v_{rms}} = \sqrt{\frac{3RT}{M}}$${v_{av}} = \sqrt{\frac{8RT}{\pi M

Vedclass · Accepted Answer

${v_{rms}} > {v_{av}} > {v_{mp}}$

Vedclass · Answer

(B) The expressions for the three speeds of a gas at temperature $T$ are given by:${v_{rms}} = \sqrt{\frac{3RT}{M}}$${v_{av}} = \sqrt{\frac{8RT}{\pi M}}$${v_{mp}} = \sqrt{\frac{2RT}{M}}$Comparing the coefficients:${v_{rms}} = \sqrt{3} \cdot \sqrt{\frac{RT}{M}} \approx 1.732 \cdot \sqrt{\frac{RT}{M}}$${v_{av}} = \sqrt{\frac{8}{3.14}} \cdot \sqrt{\frac{RT}{M}} \approx \sqrt{2.546} \cdot \sqrt{\frac{RT}{M}} \approx 1.596 \cdot \sqrt{\frac{RT}{M}}$${v_{mp}} = \sqrt{2} \cdot \sqrt{\frac{RT}{M}} \approx 1.414 \cdot \sqrt{\frac{RT}{M}}$Thus,the relationship is ${v_{rms}} > {v_{av}} > {v_{mp}}$.

For a gas at a temperature $T$,the root-mean-square velocity ${v_{rms}}$,the most probable speed ${v_{mp}}$,and the average speed ${v_{av}}$ obey the relationship:

Similar Questions

Temperature of an ideal gas, initially at $27^{\circ} C$, is raised by $6^{\circ} C$. The rms velocity of the gas molecules will

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 root mean square speed of the molecules of a diatomic gas is $v$. When the temperature is doubled,the molecules dissociate into two atoms. The new root mean square speed of the atom is

The temperature of an ideal gas is increased from $100 \ K$ to $400 \ K$. If '$x$' is the root mean square velocity of its molecules at $100 \ K$,what is the new root mean square velocity?

The $rms$ speed of a gas at room temperature of $27^{\circ}C$ is found to be $412 \ m/s$. The gas is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module