The root mean square velocity of an ideal gas | vedclass

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

Question

(D) The root mean square velocity $(U)$ is given by the formula $U = \sqrt{\frac{3RT}{M}}$.Since $PV = nRT = \frac{m}{M}RT$,we have $P = \frac{m}{V} \

Vedclass · Accepted Answer

$1/\sqrt{d}$

Vedclass · Answer

(D) The root mean square velocity $(U)$ is given by the formula $U = \sqrt{\frac{3RT}{M}}$.Since $PV = nRT = \frac{m}{M}RT$,we have $P = \frac{m}{V} \cdot \frac{RT}{M} = d \cdot \frac{RT}{M}$,where $d$ is the density.Thus,$\frac{RT}{M} = \frac{P}{d}$.Substituting this into the velocity formula,we get $U = \sqrt{\frac{3P}{d}}$.At constant pressure $(P)$,$U \propto \frac{1}{\sqrt{d}}$.

The root mean square velocity of an ideal gas at constant pressure varies with density $(d)$ as:

Similar Questions

For $1 \ mol$ of a gas,the average kinetic energy is $E$. Then the root mean square velocity $U_{rms}$ of the gas is:

At what temperature $T$ will the average speed of $CO_2$ gas be $9.0 \times 10^4 \ cm \ s^{-1}$ (in $K$)?

What is the Maxwell-Boltzmann distribution?

What is the kinetic energy (in $J \ mol^{-1}$) of one mole of an ideal gas (molar mass $= 0.1 \ kg \ mol^{-1}$) if its rms velocity is $4 \times 10^2 \ ms^{-1}$ at $T(K)$?

Explain the following terms:
$(i) u_{mp}$
$(ii) u_{av}$
$(iii) \overline{u}^2$
$(iv) u_{rms}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module