List of top Physics Questions on kinetic theory

In a mixture of gases, the average number of degrees of freedom per molecule is 6. If the rms speed of the molecule is $c$, what is the velocity of sound in the gas?

A gaseous mixture contains 2 moles of monatomic gas and 2 moles of diatomic gas at a temperature of 500 K. The total internal energy of the gaseous mixture is
(Atmospheric pressure = $10^5$ Pa and universal gas constant = $8.3 \, J mol^{-1} K^{-1}$)

The equation for the RMS velocity is given as \[ v_{\text{rms}} = \sqrt{\frac{3RT}{M_0}} \] where $ R $ is the gas constant, $ T $ is the temperature, and $ M_0 $ is the molecular mass. If the temperature is increased, find the new RMS velocity $ v_{\text{rms}} $ when the temperature is doubled.}

If $ n $ is the number density and $ d $ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e., mean free path) is represented by:

At which temperature will the r.m.s. velocity of a hydrogen molecule be equal to that of an oxygen molecule at $ 47^\circ \text{C} $?

The average kinetic energy of a molecule of the gas is

Heat energy of 735J is given to a diatomic gas allowing the gas to expand at constant pressure Each gas molecule rotates around an internal axis but do not oscillate The increase in the intemal energy of the gas will be :

The root mean square velocity of molecules of gas is

A message signal of frequency $5 \,kHz$ is used to modulate a carrier signal of frequency $2\, MHz$ The bandwidth for amplitude modulation is:

Given below are two statements :
Statement I : The temperature of a gas is $-73^{\circ} C$ When the gas is heated to $527^{\circ} C$, the root mean square speed of the molecules is doubled.
Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.
In the light of the above statements, choose the correct answer from the options given below:

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is:-

Ratio between rms speed of Ar to the most probable speed of $O^2$ at $27\degree C$ is

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 the third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed ($ V_{\text{rms}} $) and choose the correct answer from the options given below:

A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :

The relation between root mean square speed $(v_{rms})$ and most probable speed ($v_p$) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be

7 mol of a certain monoatomic ideal gas undergoes a temperature increase of 40 K at constant pressure. The increase in the internal energy of the gas in this process is:
(Given R = 8.3 JK^–1 mol^–1)

A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be :
(Given $\pi$ = 3.14)

A vessel contains $14 g$ of nitrogen gas at a temperature of $27°C$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be:

Take $R=8.32 J-mol^{-1}K^{-1}$

According to kinetic theory of gases,
A. The motion of the gas molecules freezes at 0°C
B. The mean free path of gas molecules decreases if the density of molecules is increased.
C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.
D. Average kinetic energy per molecule per degree of freedom is $\frac{3}{2}k_BT$ (for monoatomic gases).
Choose the most appropriate answer from the options given below:

Five gas molecules chosen at random are found to have speeds of 500, 600, 700, 800 and 900m/s.

Consider two ideal diatomic gases $A$ and $B$ at some temperature $T$. Molecules of the gas A are rigid , and have an mass $m$. Molecules of the gas $B$ have an additional vibrational mode, and have a mass $\frac{m}{4}.$ The ratio of the specific heats $(C^{A}_{V}$ and $C^{B}_{V})$ of gas $A$ and $B$, respectively is :

The average kinetic energy of an ideal gas molecule in SI unit at 25^∘C will be:

The molecules of a given mass of a gas have r.m.s. velocity of 200m s⁻1 at 27^∘C and 1.0×10⁵N m⁻2 pressure. When the temperature and pressure of the gas are respectively 127^∘C and 0.05×10⁵N m⁻2, the r.m.s. velocity of its molecules in m s⁻1 is:

A $15\, g$ mass of nitrogen gas is enclosed in a vessel at a temperature $27^{\circ}C$. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/ K mole]

A vertical closed cylinder is separated into two parts by a frictionless piston of mass $m$ and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $\ell_1$, and that below the piston is $\ell_2$ , such that $\ell_1$>$\ell_2$. Each part of the cylinder contains $n$ moles of an ideal gas at equal temperature $T$. If the piston is stationary, its mass, $m$, will be given by : (R is universal gas constant and $g$ is the acceleration due to gravity)