Kinetic Theory of an Ideal Gas

Correct gas equation is:

The ratio amongst most probable velocity, mean velocity and root mean square velocity is given by

A closed flask contains water in all its three states, solid, liquid and vapour at $\mathrm{}\mathrm{}\mathrm{}\mathrm{}0°C$ . In this situation, the average kinetic energy of water molecules will be

At what temperature, the $rms$ velocity of helium molecules will be equal to that of hydrogen molecules at NTP?

For an atmosphere of helium at$27 °\mathrm{C}$, speed of sound is $v_0$. Find the speed of sound for an atmosphere of hydrogen ($H_2)$ at $27 °\mathrm{C}$.

By what factor the rms velocity will change if the temperature is raised from $27° \mathrm{C}$ to $327° \mathrm{C}$?

For an atmosphere of Helium, speed of sound is $v_0$. Find the speed of sound for an atmosphere of Hydrogen$\left(H_2\right)$ at $27 °\mathrm{C}$

Why balloon reduced its size when it is kept in refrigerator?

The temperature of a gas is $-50 °\mathrm{C}$. To what temperature the gas should be heated so that the rms speed is increased by $3$ times?

If the r.m.s speed of chlorine molecule is $490 \mathrm{m} {\mathrm{s}}^{-1}$ at ${27}^{\mathrm{o}}\mathrm{C}$, the r.m.s speed of argon molecules at the same temperature will be (Atomic mass of argon $=39.9 \mathrm{u}$, molecular mass of chlorine $=70.9 \mathrm{u}$)

The $\mathrm{rms}$ speed of oxygen molecule in a vessel at particular temperature is ${\left(1+\frac{5}{x}\right)}^{\frac{1}{2}}v,$ when $v$ is the average speed of the molecule. The value of $x$ will be:

(take $\pi =\frac{22}{7}$)

A gas mixture consists of $2$ moles of oxygen and $4$ moles of neon at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system will be:

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed $\left(v_{rms}\right)$ and choose the correct answer from the options given below:

The root mean square speed of molecules of nitrogen gas at $27°\mathrm{C}$ is approximately: (Given mass of a nitrogen molecule $=4.6\times {10}^{-26} \mathrm{kg}$ and take Boltzmann constant $k_B=1.4\times {10}^{-23}\mathrm{J} {\mathrm{K}}^{-1}$ )

The number of air molecules per ${\mathrm{cm}}^3$ is increased from $3\times {10}^{19}$ to $12\times {10}^{19}.$ The ratio of collision frequency of air molecules before and after the increase in number respectively is :

The temperature of an ideal gas is increased from $200 \mathrm{K}$ to $800 \mathrm{K}$. If r.m.s. speed of gas at $200 \mathrm{K}$ is $v_0$. Then, r.m.s. speed of the gas at $800 \mathrm{K}$ will be:

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at $27°\mathrm{C}$ is

Ratio between rms speed of $\mathrm{Ar}$ to the most probable speed of ${\mathrm{O}}_2$ at $27° \mathrm{C}$ is

Find the ratio of root-mean-square speed of oxygen gas molecules to that of hydrogen gas molecules, if temperature of both the gases are same.

Internal energy of $3$ moles of a gas having degree of freedom $6$ is equal to ($T$ is temperature) $aRT$. Then value of$a$ is