Derivation of Boyle's Law

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

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

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 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

If hot air balloon has a constant velocity say$2 \mathrm{m} {\mathrm{s}}^{-1}$going up and if its buoyant force and gravitational force get cancelled then how did the balloon get the initial force in the beginning?

Total kinetic energy of $8 \mathrm{g}$ He gas at $27° \mathrm{C}$ is

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 \mathrm{m} {\mathrm{s}}^{-1}$, then the rms speed of Helium molecules at the same temperature is

Two gases $A$ and $B$ are having molar mases of $M_1$ and $M_2$ and temperatures $T_1$ and $T_2$ respectively. The RMS speed of gas $A$ is twice the RMS speed of gas $B$. If the ratio of $M_1$ to $M_2$ is $2:1$, then the ratio of $T_1$ to $T_2$ is

The RMS speed of molecules of an ideal gas at $27 °\mathrm{C}$ is $200 \mathrm{m} {\mathrm{s}}^{-1}$. When the temperature is increased to $327 °\mathrm{C}$, the RMS speed of the molecules is changed to

At what temperature the root-mean-square speed of nitrogen at $27 °\mathrm{C}$ would be tripled?

At a certain temperature, the rms velocity for ${\mathrm{O}}_2$ is $400 \mathrm{m} {\mathrm{s}}^{-1}$. At the same temperature, the rms velocity for ${\mathrm{H}}_2$ molecules will be