List of top Physics Questions on kinetic theory

The mean free path of moving gas molecules is expressed as $\lambda \propto n^x d^y$ where $n$ is the number of molecules per unit volume and $d$ is the size of the molecules. Then the values of $x$ and $y$ respectively, are
The ratio of specific heats $C_{p}/C_{v}$ for a mixture of 1 mole of helium and 1 mole of hydrogen is:
The temperature at which the rms speed of hydrogen molecules is equal to that of oxygen molecules at \(47^\circ C\) is
Keeping the number of gas molecules per unit volume as constant, if the radius of the gas molecule is doubled, then the mean free path of the gas molecules
A and B are two ideal gases. \(3\) g-mole of gas A at absolute temperature \(T_1\) and \(5\) g-mole of gas B at absolute temperature \(T_2\) have been mixed. There is no loss of energy in the process. Find the temperature of the mixture if \(T_1=300\) K and \(T_2=500\) K.
The approximate temperature at which the rms speed of Nitrogen gas molecule is \( 500 \text{ ms}^{-1} \). Gas constant \( R=8.314 \text{ J mol}^{-1} \text{K}^{-1} \), Mass number of Nitrogen = 28:
The R.M.S. speed of oxygen molecules at \(27^\circ\text{C}\) is \(v\). At \(927^\circ\text{C}\), its R.M.S. speed will be
In an isothermal process
The ratio of velocity of sound to the rms velocity of gas molecules in a diatomic gas is:
If the mean free path of a nitrogen molecule in a vessel containing nitrogen at a pressure of 2.1 atm and a temperature of $27^{\circ}C$ is $\lambda$, then its mean free path at a pressure of 1.65 atm and a temperature of $57^{\circ}C$ is:
The rms speed of oxygen molecule at some temperature is $150 \text{ ms}^{-1}$. Then the rms speed of hydrogen molecule at the same temperature is
The mean free path of a gas molecule is inversely proportional to
The mean free path of a gas molecule is inversely proportional to
The specific heat capacity of a gas at constant pressure ($C_p$) and at constant volume ($C_v$) are related as
At what temperature is the root mean square (rms) speed of oxygen molecules ($O_2$) equal to that of helium molecules ($He$) at $27^\circ\text{C}$? (Given molar mass of $O_2 = 32\text{ g/mol}$, $He = 4\text{ g/mol}$)}
The rms velocity of hydrogen molecules at 27°C is v. At what temperature will the rms velocity of oxygen molecules equal v ?
The root mean square (rms) speed of the molecules of an ideal gas at a given temperature \(T\) is \(v\). If the temperature is increased to \(4T\) and the gas dissociates into atoms, the new rms speed becomes:
Find the mass of oxygen gas with which $882\times10^{23}$ degrees of freedom are associated at N.T.P. Given: Molar mass of diatomic gas, oxygen is $32\text{ g mol}^{-1}$ and oxygen molecule possess three translational and two rotational degrees of freedom.
A vessel of volume $27 \times 10^{4}\text{ cc}$ contains a mixture of Hydrogen (molar mass $= 2\text{ g mol}^{-1}$) and Oxygen (molar mass $= 32\text{ g mol}^{-1}$) gas at standard temperature and pressure (S.T.P.). If the mass of hydrogen is $16\text{ g}$, find the mass of oxygen gas contained in the vessel.
The rms speed of gas molecules is given by:
The INCORRECT assumption in the kinetic theory of gases is
If $f$ represents the intermolecular force between molecules and $V$ is the volume occupied by the gas molecules, then at high pressure and at low temperatures, the gas shows large deviation from the ideal behaviour because the fact that
If 300 J of heat energy is used to raise the temperature of one mole of an ideal gas by 10 K at constant pressure, then heat energy required to raise its temperature by 10 K at constant volume is $(R=8.3\text{ J mol}^{-1}\text{K}^{-1})$
If the diatomic molecule is non-rigid, then its molar specific heat capacity at constant volume is
The mass of one molecule of water is approximately