A box of negligible mass containing 2 moles of an ideal gas of molar mass M and adiabatic exponent $\gamma$ moves with constant speed v on a smooth horizontal surface. If the box suddenly stops, then the change in the temperature of the gas will be:

(1) $\frac{(\mathrm{\gamma }-1){\mathrm{Mv}}^2}{4\mathrm{R}}$

(2) $\frac{{\mathrm{\gamma Mv}}^2}{2\mathrm{R}}$

(3) $\frac{{\mathrm{Mv}}^2}{2(\mathrm{\gamma }-1)\mathrm{R}}$

(4) $\frac{(\mathrm{\gamma }-1){\mathrm{Mv}}^2}{2\mathrm{R}}$

On increasing number density for a gas in a vessel, the mean free path of a gas:

(1) Decreases

(2) Increases

(3) Remains same

(4) Becomes double

Two closed containers of equal volume are filled with air at pressure ${\mathrm{P}}_0$ and temperature ${\mathrm{T}}_0$. Both are connected by a narrow tube. If one of the containers is maintained at temperature ${\mathrm{T}}_0$ and the other at temperature T, then new pressure in the container will be:

1. $\frac{2{\mathrm{P}}_0\mathrm{T}}{\mathrm{T}+{\mathrm{T}}_0}$

2. $\frac{{\mathrm{P}}_0\mathrm{T}}{\mathrm{T}+{\mathrm{T}}_0}$

3. $\frac{{\mathrm{P}}_0\mathrm{T}}{2(\mathrm{T}+{\mathrm{T}}_0)}$

4. $\frac{\mathrm{T}+{\mathrm{T}}_0}{{\mathrm{P}}_0}$

The pressures of a gas filled in the bulb of a constant volume gas thermometer at temperatures $0°\mathrm{C}$ and $100°\mathrm{C}$ are 27.50 cm and 37.50 cm of Hg respectively. At an unknown temperature, the pressure is 32.45 cm of Hg. The unknown temperature is:

1. $30°\mathrm{C}$

2. $39°\mathrm{C}$

3. $49.5°\mathrm{C}$

4. $29.6°\mathrm{C}$

A graph is plotted by taking pressure along the y-axis and centigrade temperature along the x-axis for an ideal gas at constant volume. The x-intercept of the graph is:

1. $-273.15°\mathrm{C}$

2. $-273.15 \mathrm{K}$

3. $-273°\mathrm{C}$

4. $-273 \mathrm{K}$

Heat is  associated with:

Which one of the following graphs represents the behaviour of an ideal gas?

1. 

2. 

3. 

4. 

A jar has a mixture of hydrogen and oxygen gases in the ratio of 1: 5. The ratio of mean kinetic energies of hydrogen and oxygen molecules is:

1. 1: 16

2. 1: 4

3. 1: 5

4. 1: 1

A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per O₂ molecule to that per N₂ molecule is:

1. 1: 1

2. 1: 2

3. 2: 1

4. Depends on the moments of inertia of the two molecules

A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglecting effect of gravity, pressure in the compartment is:

1. same everywhere

2. lower in the front

3. lower in the rear side

4. lower in the upper side