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Q 01 / 25
According to the kinetic theory of gases a gas consists of a very large number of tiny particles called molecules in constant random motion.
Q 02 / 25
In kinetic theory the volume of individual gas molecules is assumed to be negligible compared to the volume of the container.
Q 03 / 25
The collisions between molecules of an ideal gas and the container walls are taken to be perfectly elastic.
Q 04 / 25
In kinetic theory it is assumed that there are strong long-range attractive forces between ideal gas molecules at all times.
Q 05 / 25
Pressure of a gas on the walls of its container arises from the continuous bombardment of molecules on the walls.
Q 06 / 25
For a given ideal gas at fixed temperature the root mean square speed of molecules does not depend on the molecular mass.
Q 07 / 25
At a fixed temperature lighter gas molecules have on average higher root mean square speed than heavier molecules.
Q 08 / 25
For an ideal gas at absolute temperature T the average translational kinetic energy per molecule is proportional to T.
Q 09 / 25
If the temperature of an ideal gas is doubled at constant volume its pressure also becomes four times.
Q 10 / 25
For a given sample of ideal gas at constant pressure the volume is directly proportional to its absolute temperature.
Q 11 / 25
The ideal gas equation \(PV=nRT\) can be obtained using kinetic theory by relating pressure to the mean square speed of gas molecules.
Q 12 / 25
In kinetic theory the speed of every molecule of a gas at a given temperature is the same.
Q 13 / 25
The most probable speed the mean speed and the rms speed of molecules in a gas are all equal at any temperature.
Q 14 / 25
The Maxwell–Boltzmann speed distribution becomes narrower and shifts to lower speeds when the gas is cooled.
Q 15 / 25
If the temperature of a gas is increased the fraction of molecules having very high speeds increases.
Q 16 / 25
Mean free path of a gas molecule is the average distance it travels between two successive collisions.
Q 17 / 25
At fixed temperature and pressure the mean free path of molecules in a gas increases when the molecular diameter increases.
Q 18 / 25
For an ideal gas the internal energy depends only on the temperature and not on the volume occupied.
Q 19 / 25
For a monoatomic ideal gas the law of equipartition of energy gives \(U=\tfrac{3}{2}nRT\) for the total internal energy.
Q 20 / 25
For a diatomic ideal gas at room temperature only translational degrees of freedom contribute to internal energy.
Q 21 / 25
According to equipartition of energy each independent quadratic degree of freedom of a molecule contributes \(\tfrac{1}{2}kT\) to the average energy per molecule.
Q 22 / 25
If \(C_{V}\) is the molar heat capacity at constant volume the number of active degrees of freedom \(f\) can be written as \(f=\tfrac{2C_{V}}{R}\) for an ideal gas.
Q 23 / 25
For a fixed amount of ideal gas if the rms speed of its molecules doubles the absolute temperature of the gas becomes four times.
Q 24 / 25
In an ideal gas mixture at equilibrium all components have the same average translational kinetic energy per molecule even if their molar masses differ.
Q 25 / 25
If two different ideal gases are at the same pressure and have the same rms speed of molecules they must also have the same density.

Frequently Asked Questions

It is a theory that explains the macroscopic properties of gases (pressure, temperature, volume) in terms of the microscopic motion of gas molecules.

Gas consists of a large number of molecules in random motion; intermolecular forces are negligible except during collisions; collisions are elastic; molecular size is negligible compared to separation.

An ideal gas is a hypothetical gas that obeys the equation \(PV = nRT\) exactly at all pressures and temperatures.

Because real gases have finite molecular size and intermolecular forces, which cause deviations at high pressure and low temperature.

\(PV = nRT\), where \(P\) is pressure, \(V\) volume, \(n)\ number of moles, \(R)\ gas constant, and \(T\) absolute temperature.

\(R = 8.314, \text{J mol}^{-1}\text{K}^{-1}\).

It is the constant that relates temperature to energy at the molecular level: \(k_B = 1.38 \times 10^{-23},\text{J K}^{-1}\).

Pressure arises due to momentum transfer when gas molecules collide elastically with the walls of the container.

\(P = \frac{1}{3}\frac{Nm}{V}\overline{c^2}\).

Temperature is a measure of the average translational kinetic energy of gas molecules.

\(\overline{E_k} = \frac{3}{2}k_B T\).

No, it depends only on temperature.

It is defined as \(c_{\text{rms}} = \sqrt{\overline{c^2}} = \sqrt{\frac{3RT}{M}}\).

It is the speed possessed by the maximum number of molecules at a given temperature.

It is the average speed of all molecules in a gas.
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