Kinetic theory of gases practice · Mixed difficulty

Calculate the r.m.s. velocity of air molecules at S.T.P. Given density of air at S.T.P. is $1.296 \mathrm{~kg} \mathrm{~m}^{-3}$.

When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume, its temperature increases by $\Delta T$. The heat required to produce the same change in temperature, at a constant pressure is

A diatomic molecule has how many degrees of freedom

A vessel contains $14 \mathrm{~g}$ of nitrogen gas at a temperature of $27^{\circ} \mathrm{C}$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be:

Take $R=8.32 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$.

The temperature of the gas is a measure of

How many times a diatomic gas should be expanded adiabatically so as to reduce the root mean square velocity to half

Find out the temperature of oxygen at which $v_{r m s}$ of oxygen is equal to $v_{r m s}$ of hydrogen at $27^{\circ} \mathrm{C}$.

$4.0 \mathrm{~g}$ of helium occupies $22400 \mathrm{~cm}^3$ at STP. The specific heat capacity of helium at constant pressure is $5.0\, \mathrm{cal} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$. Calculate the speed of sound in helium at STP.

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature $T$ ?(${k_B}$ is Boltzmann constant)

For an ideal gas of diatomic molecules

The correct relation between the degrees of freedom $f$ and the ratio of specific heat $\gamma$ is

Supposing the distance between the atoms of a diatomic gas to be constant, its specific heat at constant volume per mole (gram mole) is

At a pressure of $24 \times {10^5}\,\,\mathrm{dyne/c}{\mathrm{m}^\mathrm{2}},$ the volume of ${O_2}$ is 10 litre and mass is 20 gm. The rms velocity is [in m/sec]

Vessel $A$ is filled with hydrogen while vessel $B,$ whose volume is twice that of $A,$ is filled with the same mass of oxygen at the same temperature. The ratio of the mean kinetic energies of hydrogen and oxygen is

The rms velocity of the molecules in a sample of helium is $5 / 7$ in that of the molecules in a sample of hydrogen. If the temperature of hydrogen sample is $0^{\circ} {C}$. The temperature of the helium sample is nearly

In a mixture of gases at a fixed temperature

Assertion (A) : If a gas container is placed in a moving train, the temperature of gas will increase.

Reason (R) : Kinetic energy of gas molecules will increase.

Determine the absolute gas temperature at which the root mean square speed of helium molecules exceeds their most probable speed by $200 \mathrm{~m} / \mathrm{s}$.

Assertion: The ratio of specific heat gas at constant pressure and specific heat at constant volume for a diatomic gas is more than that for a monatomic gas.
Reason: The molecules of a monatomic gas have more degrees of freedom than those of a diatomic gas.

The average degree of freedom per molecule for a gas is 6 . The gas performs $25 \mathrm{~J}$ of work when it expands at constant pressure. The heat absorbed by the gas is

A tyre kept outside in sunlight bursts off after sometime because of

Consider a sample of oxygen at $300 \mathrm{~K}$. Find the average time taken by a molecule to travel a distance equal to the diameter of the earth.

The root mean square velocity of a gas molecule of mass $m$ at a given temperature is proportional to

Two containers A and B are such that,$V_A=0.10 \mathrm{~m}^3, P_A=1.40 \mathrm{MPa}, V_B=0.15 \mathrm{~m}^3, P_B=0.7 \mathrm{MPa}$

After opening the tap, final pressure in the containers is (Assume temperature of A and B are same)

The amount of heat required to raise the temperature of 1 mole of a monoatomic gas from $20^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$ at constant volume is $H$. Then, the amount of heat required to raise the temperature of $2 \mathrm{~mol}$ of a diatomic gas from $20^{\circ} \mathrm{C}$ to $25^{\circ} \mathrm{C}$ at constant pressure is

In case of hydrogen and oxygen at NTP, which of the following is the same of both ?

The average kinetic energy of a gas molecule can be determined by knowing

A mixture of 2 moles of helium gas (atomic mass = $4\;amu$), and 1 mole of argon gas (atomic mass = $40amu$) is kept at $300K$ in a container. The ratio of the $rms$ speeds $\left[ {\frac{{{V_{rms}}\left( {\mathrm{helium}} \right)}}{{{V_{rms}}\left( {\mathrm{argon}} \right)}}} \right]$ is

Consider a gas with density $\rho$ and ${\bar c}$ as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity $v,\;$ then the pressure exerted by the gas is

The kinetic energy of emitted electron is $E$ when the light incident on the metal has wavelength $\lambda$. To double the kinetic energy, the incident light must have wavelength :