Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$,while Box $B$ contains one mole of helium at temperature $(7/3)T_0$. The boxes are then put into thermal contact with each other,and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of the boxes). The final temperature of the gases,$T_f$,in terms of $T_0$ is:

$CO_2$ $(O-C-O)$ is a triatomic gas. The mean kinetic energy of one gram of the gas will be (where $N$ is Avogadro's number,$k$ is Boltzmann's constant,and the molecular weight of $CO_2 = 44$).

The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting,movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and $1$ moles of an ideal gas,respectively. In the left compartment,the piston is attached by a spring with spring constant $k$ and natural length $\frac{2L}{5}$. In thermodynamic equilibrium,the piston is at a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions,if the pressure in the right compartment is $P = \frac{kL}{A} \alpha$,then the value of $\alpha$ is:

An ideal gas is filled in a closed container and the container is moving with uniform acceleration in the horizontal direction. Neglect gravity. The pressure inside the container is ...............

The oxygen molecule has a mass of $5.30 \times 10^{-26} \; kg$ and a moment of inertia of $1.94 \times 10^{-46} \; kg \cdot m^{2}$ about an axis through its centre perpendicular to the line joining the two atoms. Suppose the mean speed of such a molecule in a gas is $500 \; m/s$ and that its kinetic energy of rotation is two-thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.

$A$ diatomic gas of molecular weight $30 \, g/mol$ is filled in a container at $27 \, ^\circ C$. It is moving at a velocity of $100 \, m/s$. If it is suddenly stopped,the rise in temperature of the gas is: