Kinetic Theory

Which of the following is equivalent to 1 Pascal?

At what temperature does the volume of an ideal gas theoretically become zero according to Charles's Law?

The 'Equation of State' for a perfect gas relates which of the following?

If the number of molecules in a container is doubled at constant volume and temperature, the pressure will:

A gas at $27^{\circ} C$ has a volume $V$ and pressure $P$. On heating, its pressure is doubled and volume is tripled. What is the final temperature?

The absolute temperature of a gas is increased 4 times and its pressure is increased 2 times. What happens to its volume?

A vessel of volume $V$ contains a mixture of $1 \text{ mole}$ of Hydrogen and $1 \text{ mole}$ of Oxygen at temperature $T$. What is the pressure of the mixture?

Three containers of equal volume contain $3\text{ g}$ of H$_2$, $8\text{ g}$ of O$_2$ and $14\text{ g}$ of N$_2$ respectively at the same temperature. Which container has the highest pressure?

The density of air at $S.T.P.$ is $1.29\text{ kg/m}^3$. What will be its density at $127^{\circ}C$ and $0.5\text{ atm}$ pressure?

The equation of state for a certain gas is $P(V - nb) = nRT$. If $1\text{ mole}$ of this gas is expanded isothermally from $V_1$ to $V_2$, the work done is:

The translational kinetic energy of a molecule is independent of:

Two gases are kept at the same temperature. Gas 1 has molecules of mass $m$ and Gas 2 has molecules of mass $2m$. The ratio of their average kinetic energies is:

If the pressure of an ideal gas is kept constant while its absolute temperature is tripled, the rms speed will increase by factor:

Which of the following is equivalent to the absolute zero temperature?

In the sequence of physical quantities shown in the diagram for an ideal gas, Node A represents the Absolute Temperature ($T$), Node B represents the Average Translational Kinetic Energy per molecule ($\bar{E}$), and Node C represents the Root Mean Square speed ($v_{rms}$). If the system transitions such that the value at Node A is tripled and the gas species is changed from Helium (atomic mass $4\ u$) to Hydrogen (molecular mass $2\ u$), find the ratio of the final value at Node C to its initial value.

According to kinetic theory, at absolute zero, which of the following is true for an ideal gas?

The temperature at which the $v_{rms}$ of a gas molecule is half of its value at $0^{\circ}C$ is:

The total translational kinetic energy of $n$ moles of an ideal gas at temperature $T$ is $E$. If the number of moles is doubled and the temperature is halved, what is the new total translational kinetic energy?

Which of the following describes the behavior of $v_{rms}$ as a function of molar mass $M$ at a constant temperature?

A cylinder contains $20\ kg$ of Nitrogen at $10^6\ Pa$. If the root mean square speed is doubled by heating the gas at constant volume, what is the new pressure?

Which of the following is the correct value of $\gamma$ for a gas whose molecules have 5 degrees of freedom?

The Law of Equipartition of Energy is valid for systems that are in:

The average kinetic energy per mole of any ideal gas depends ONLY on its:

The total energy of 1 mole of Helium gas at $300 K$ is:

A gas molecule with 6 degrees of freedom has a molar heat capacity at constant pressure $C_p$ equal to:

Which of the following statements about the law of equipartition of energy is FALSE?

The internal energy of a system of 1 mole of a monoatomic gas and 1 mole of a diatomic gas (rigid) at temperature $T$ is:

A certain gas molecule has $f$ degrees of freedom. The ratio of the heat required to raise the temperature of $n$ moles by $\Delta T$ at constant pressure to that at constant volume is $1.4$. Find $f$.

Two moles of an ideal diatomic gas ($f=5$) are heated so that its absolute temperature is tripled. If the process is such that no heat is exchanged with the surroundings, but the gas does work, what is the change in internal energy?

A polyatomic gas has 3 translational, 3 rotational, and 2 vibrational degrees of freedom. The ratio $C_p/C_v$ is:

If the mean free path of gas A is twice that of gas B at the same number density, then the ratio of their molecular diameters ($d_A/d_B$) is:

The mean free path is related to the macroscopic density (mass/volume) $\rho$ as:

If the diameter of a molecule is $d$, the effective 'collision volume' swept by a molecule moving a distance $L$ is roughly:

Which of the following would NOT change the mean free path of a gas in a closed container?

If the collision frequency is denoted by $\nu$ and the average speed of the gas molecules is $v$, the mean free path $\lambda$ is:

If a gas undergoes a process where its mass density $\rho$ remains constant, how does the mean free path behave?

On average, how many collisions does a molecule undergo while traveling a total distance equal to ten times its mean free path?

For a given gas at pressure $P$ and temperature $T$, the mean free path is $\lambda$. If the gas is taken through a process where $T/P^2 = \text{constant}$, the mean free path $\lambda$ will be proportional to:

If we increase the temperature of a gas at constant volume, which of the following remains constant?

If the mean free path of a gas at $1$ atm is $\lambda$, what will be the mean free path at $5$ atm if the temperature is also increased such that the RMS speed of the molecules doubles?

In the kinetic theory of gases, the molecules are considered to be:

The molar mass of Oxygen ($O_2$) gas is 32 g/mol. What is the mass of one molecule of Oxygen?

The SI unit of the Boltzmann constant is:

Which constant is same for all gases at a given temperature?

The value of Avogadro's number $N_A$ is approximately:

If the temperature of a gas is increased from $200 \text{ K}$ to $800 \text{ K}$, the average kinetic energy of the molecules becomes:

The ratio of the RMS speed of Helium to that of Neon at the same temperature is: (Atomic mass of $He = 4$, $Ne = 20$)

In a Maxwell-Boltzmann distribution, the ratio of the most probable speed, the average speed, and the root mean square speed is:

A gas expands such that $PT^2 = \text{constant}$. The coefficient of volume expansion of the gas is:

A gas mixture contains molecules of types A, B, and C with masses $m_A > m_B > m_C$. At thermal equilibrium, which molecules have the highest average kinetic energy?

The internal energy of an ideal gas consists only of:

The dimensions of the universal gas constant $R$ are:

If the temperature of a gas in a closed container is increased, the pressure increases because:

The number of molecules in $22.4\ L$ of any gas at STP is:

The number of degrees of freedom of a diatomic molecule like $O_2$ at very high temperatures, where vibrational motion also occurs, is:

The pressure of a gas is $P = \frac{1}{3} \rho v_{rms}^2$. If the density $\rho$ is doubled and $v_{rms}$ is halved, the new pressure will be:

If the mean free path of a gas is $10^{-7}\text{ m}$ at a pressure of $1\text{ atm}$, what will be the mean free path at $2\text{ atm}$ pressure if the temperature remains constant?

A flask contains argon and chlorine in the ratio 2:1 by mass at $27^{\circ}C$. The ratio of average kinetic energy per molecule of argon to chlorine is:

For a gas, if $C_p - C_v = R$ and $C_p/C_v = 1.67$, the gas atomicity is:

The relation between the pressure $P$ and kinetic energy per unit volume $E$ of an ideal gas is:

If $v_{rms}$ of a gas molecule is $v$, what will be the $v_{rms}$ if the temperature is doubled and mass is halved?

The total kinetic energy of a gas is a measure of its:

The pressure-volume product ($PV$) for a fixed mass of gas at constant temperature is:

Specific heat of a gas at constant volume ($C_v$) for a monatomic gas is:

A thermally insulated rigid container of negligible heat capacity holds $1\text{ mole}$ of a monatomic ideal gas of molar mass $M$. The entire container is moving with a constant speed $v_0$. If the container is suddenly brought to rest and all its bulk kinetic energy is converted into the internal energy of the gas, the resulting increase in the temperature $\Delta T$ of the gas is:

A system consists of two identical vessels, $A$ and $B$, connected by a thin tube of negligible volume. Initially, the system contains an ideal gas at pressure $P_0$ and temperature $T$. If vessel $A$ is maintained at temperature $T$ while vessel $B$ is heated and maintained at temperature $2T$, what will be the new equilibrium pressure $P$ of the gas?

The expression for the pressure of a gas is $P = \frac{1}{3} n m v_{rms}^2$. If $n$ is the number of molecules per unit volume, what is $nm$?

If $R$ is universal gas constant and $N_A$ is Avogadro number, then the Boltzmann constant $k_B$ is given by:

A gas at $300$ K has a pressure $P$. If the volume is increased by $10\%$ and temperature is increased to $330$ K, the new pressure is:

Which of the following speed is the highest for a gas at a specific temperature?

According to kinetic theory, at absolute zero temperature, the specific heat of a gas would be:

For a polyatomic gas with $f$ degrees of freedom, the ratio $\gamma$ is:

The specific heat of an ideal gas at constant volume is independent of:

For 1 mole of a monoatomic gas, the internal energy is $U$. If the temperature is doubled, the new internal energy is:

Molar specific heat at constant volume for a gas is $C_v$. If we use $c_v$ to denote specific heat per unit mass and $M$ for molar mass, then $c_p - c_v$ is:

For an ideal gas, the ratio $\frac{R}{C_v}$ is equal to:

The molar heat capacity of Oxygen at very low temperatures (where only translation is active) is:

The molar specific heat capacity of a diatomic gas at constant volume is $C_v$. When vibrational modes are neglected, $C_v = 5R/2$. If vibrational modes are included, $C_v$ increases by $R$ for each mode. For a molecule like $HCl$, how many modes are possible?

The molar heat capacity of a gas at constant pressure is $C_p = 7R/2$. The gas is most likely:

A mixture of 1 mole of Nitrogen and 1 mole of Helium is kept in a container. The ratio of their average kinetic energies per molecule is: