JEE Main 2026 — Physics Thermodynamics

Consider two boxes containing ideal gases $A$ and $B$ such that their temperatures, pressures and number densities are same. The molecular size of $A$ is half of that of $B$ and mass of molecule $A$ is four times that of $B$. If the collision frequency in gas $B$ is $32 \times 10^{18} / \mathrm{s}$ then collision frequency in gas $A$ is $\_\_\_\_$ $/ \mathrm{s}$.

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from $27^{\circ} \mathrm{C}$ to $87^{\circ} \mathrm{C}$. The rate of consumption of the gas is $\_\_\_\_$ $\mathrm{g} / \mathrm{s}$. (Take heat of combustion of gas $=5.0 \times 10^{4} \mathrm{~J} / \mathrm{g}$) specific heat capacity of water $=4200 \mathrm{~J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$

The internal energy of a monoatomic gas is 3 nRT. One mole of helium is kept in a cylinder having internal cross section area of $17 \mathrm{~cm}^{2}$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by $4^{\circ} \mathrm{C}$, then the piston will move $\_\_\_\_$ cm. (atmospheric pressure $=10^{5} \mathrm{~Pa}$)

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P, V, T$. Heating is started from left side until pressure changes to $\dfrac{27P}{8}$. If initial volume of each compartment was $9$ litres then the final volume in right-hand side compartment is __________ litres. (for this ideal gas $C_P/C_V = 1.5$)

One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure $P$ and volume $V$ of the mixture. The temperature of the mixture is _____.