Assertion: An ideal gas is enclosed within a container fitted with a piston. When volume of this enclosed gas is increased at constant temperature, the pressure exerted by the gas on the piston decreases.

Reason: In the above situation, the rate of molecules striking the piston decreases. If the rate ạt which molecules of a gas having same average speed striking a given area of the wall decreases, the pressure exerted by gas on the wall decreases.

Assertion: Different gases at the same conditions of temperature and pressure have same root mean square speed.

Reason: Average K.E. of gas is inversely proportional to temperature in Kelvin.

Assertion: The root mean square velocity of molecules of a gas having Maxwellian distribution of velocities is higher than their most probable velocity at any temperature.

Reason: A very small number of molecules of a gas possessing very large velocities increases the root mean square velocity without affecting the most probable velocity.

Assertion: Two different gases having same temperature always have molecules with same RMS
speed.

Reason: The average translational kinetic energy per mole for each gas is $\frac{3}{2}KT$ (where, $K=$Boltzmann constant, $T=$temperature in Kelvin).

Assertion: The pressure of a gas filled in a cylinder fitted with an immovable piston is increased by raising its temperature.

Reason: On raising the temperature, greater momentum is transferred to the wall of the container per second.

Assertion: It is possible for both the pressure and volume of a monoatomic ideal gas of a given amount to change simultaneously without causing the internal energy of the gas to change.

Reason: The internal energy of an ideal gas of a given amount remains constant if temperature does not change. It is possible to have a process in which pressure and volume are changed such that temperature remains constant.

Assertion: Equal moles of helium and oxygen gases are given equal quantities of heat at constant volume. There will be a greater rise in the temperature of helium as compared to that of oxygen.

Reason: The molecular weight of oxygen is more than the molecular weight of helium.

One mole of an ideal gas goes from an initial state $A$ to final state $B$ via two processes. It first undergoes isothermal expansion from volume $V$ to $3 V$ and then its volume is reduced from $3 V$ to $V$ at constant pressure. The correct $PV$ diagram representing the two processes is: 

In the given $(V-T)$ diagram, what is the relation between pressure $P_1$ and $P_2$?