Average and Root Mean Square Speeds of the Gas Molecules

The $\mathrm{rms}$ speed of an ideal gas is $c$. The volume of the gas is doubled keeping its temperature unchanged. The $\mathrm{rms}$ speed will now be

The ratio of the most probable velocity $\left(c_{\mathit{m}}\right)$ and $\mathrm{rms}$ velocity $\left(c_{\mathrm{rms}}\right)$ of the molecules of a given gas at a given temperature is

There is a mixture of hydrogen and oxygen in a vessel. The rms velocity of oxygen molecules is

The average velocity of a gas molecule is $\overline{c}, \mathrm{rms}$ velocity $c_{\mathrm{rms}}$ and the most probable velocity, $c_{\mathit{m}}$. Then

Calculate the most probable speed, mean speed and rootmean-square speed for nitrogen at $300 \mathrm{K}$.

In a closed vessel one gm mole of nitrogen is kept at a temperature of $300 \mathrm{K}$. What is the amount of heat required to raise the temperature of the gas, so that the $\mathrm{r}.\mathrm{m}.\mathrm{s}.$ Speed of molecules becomes $3$ Times its initial value. Given: $R=2 \mathrm{cal}/\mathrm{k}-\mathrm{mol}$.

$2 \mathrm{gm} \mathrm{mol}$ of helium having $\mathrm{r}.\mathrm{m}.\mathrm{s}.$ speed of molecules $1000 {\mathrm{ms}}^{-1}$ and $0.5 \mathrm{gm} \mathrm{mol}$ of nitrogen having $\mathrm{r}.\mathrm{m}.\mathrm{s}.$ speed $3000 {\mathrm{ms}}^{-1}$ are mixed in thermally insulated container. What are the $\mathrm{r}.\mathrm{m}.\mathrm{s}.$ speeds of helium and nitrogen molecules after equilibrium is reached?

Kinetic temperature of small particle is the temperature of a gas at equilibrium, whose most probable speed is the speed of the particle. Find the kinetic temperature of a proton of energy $1 \mathrm{mev}$ and that of a ball of mass $250 \mathrm{gm}$ moving with a velocity of $10{ \mathrm{ms}}^{-1}$.

The average translational energy and the $\mathrm{rms}$ speed of molecules in a gas at $300 \mathrm{K}$ are $6.21\times {10}^{-21} \mathrm{J}$ and $484 \mathrm{m}{ \mathrm{s}}^{-1}$ respectively. What are the corresponding values at $600 \mathrm{K}$ (assuming ideal gas behaviour)?

Calculate the r.m.s. speed of smoke particles of mass $5\times {10}^{-17} \mathrm{kg}$in Brownian motion in air at $\mathrm{NTP}$. Given : Boltzmann constant $k=1.38\times {10}^{-23}{\mathrm{JK}}^{-1}$.

Calcultate the density of an ideal gas at $\mathrm{S}.\mathrm{T}.\mathrm{P}.$ if $\mathrm{r}.\mathrm{m}.\mathrm{s}$ velocity of molecules be $0.5 \mathrm{km}/\mathrm{s}$. What will be the density of the gas at $21°\mathrm{C}$, the pressure remaining the same? (Assume 1 standard atmosphere $={10}^5 \mathrm{N}/{\mathrm{m}}^2$).

Calculate the total $\mathrm{K}.\mathrm{E}.$ of the molecules in $16 g$ of $O_2$ gas at $27°\mathrm{C}$. $R=8.31$ joule ${{}^{\circ }C}^{-1}{ \mathrm{mole}}^{-1}$.

At $0°\mathrm{C}$ and ${10}^{-2}$ Atmospheric pressure, the density of a gas is $1.24\times {10}^{-2} \mathrm{kg}{ \mathrm{m}}^{-3}$. Find the r m s speed of the gas molecules and its molecular mass.

Given that the gas constant $R=8.3$ joule per $°C$ and the atomic mass of chlorine is $35.5$, find the $\mathrm{rms}$ speed of chlorine molecules at $0°\mathrm{C}$.

At what temperature is the $\mathrm{rms}$ speed of hydrogen molecule equal to that of a carbon dioxide molecule at $57°\mathrm{C}$? A carbon dioxide molecule is about $22$ times heavier than a hydrogen molecule.

What is most probable speed of the gas molecules? Compare its value with the mean and $\mathrm{r}.\mathrm{m}.\mathrm{s}.$ speeds of the gas molecules.

The earth has an atmosphere of different gases like nitrogen, oxygen etc. But moon has no atmosphere Explain.

The average velocity of the molecules of a gas must be zero if the gas as a whole and the container are not in translational motion. How is it possible that the average speed of molecules is not zero?

What will be the percentage change in the $\mathrm{rms}$ velocity of gas molecules when its pressure is doubled keeping temperature constant.

Show the expressions for most probable speed, mean speed and $\mathrm{r}.\mathrm{m}.\mathrm{s}.$ speed and find their relative magnitudes.