A monoatomic gas at a pressure $P,$ having a volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V.$ The final pressure of the gas is (take $\gamma = \frac{5}{3}$)

The mean free path of molecules of a gas (radius $r$) is inversely proportional to

One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure. The change in internal energy of the gas during the transition is

The ratio of the specific heat $\frac{C_P}{C_V} = \gamma$ in terms of degrees of freedom $(n)$ is given by

Two non-mixing liquids of densities ρ and nρ (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the denser liquid. The density d is equal to

The molecules of a given mass of a gas have rms velocity of $200$ ms$^{-1}$ at $27^{\circ}C$ and $1.0 \times 10^{5}$ Nm$^{-2}$ pressure. When the temperature and pressure of the gas are, respectively, $127^{\circ}C$ and $0.05 \times 10^{5}$ Nm$^{-2},$ the rms velocity of its molecules in $$ms$^{-1}$ is

A gas mixture consists of 2 moles of O$_2$ and 4 moles of Ar at temperature $T.$ Neglecting all vibrational modes, the total internal energy of the system is

The volume $(V)$ of a monatomic gas varies with its temperature $(T)$, as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? Given: $$Mass of oxygen molecule $(m) = 2.76 \times 10^{-26}$ kg$,$Boltzmann's constant $k_B = 1.38 \times 10^{-23}$ J K$^{-1}$

A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy ($K_t$) as well as rotational kinetic energy ($K_r$) simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere is

Increase in temperature of a gas filled in a container would lead to:

A cylinder contains hydrogen gas at pressure of $249$ kPa and temperature $278 K.$ Its density is $(R = 8.3$ J mol$^{-1}$ K$^{-1}):$

The average thermal energy for a mono-atomic gas is:$\newline (k_B$ is Boltzmann constant and $T,$ absolute temperature$)$

The mean free path for a gas, with molecular diameter $d$ and number density $n$ can be expressed as:

Match Column - I and Column - II and choose the correct match from the given choices.

The volume occupied by the molecules contained in $4.5$ kg water at STP, if the intermolecular forces vanish away, is:

The temperature of a gas is $-50^\circ C.$To what temperature the gas should be heated so that the rms speed is increased by 3 times?

The following graph represents the T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures $P_1, P_2, P_3$ compared with those of Charles’s law represented as dotted lines. Then the correct relation is: