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 $\_\_\_\_$ /s.

Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $100^{\circ} \mathrm{C}$ and $40^{\circ} \mathrm{C}$ respectively. Given the thermal conductivity of $\operatorname{rod} x$ is three times of that of $\operatorname{rod} y$, the temperature at junction points $B$ and $E$ are (close to):

The volume of an ideal gas increases 8 times and temperature becomes $(1 / 4)^{\text {th }}$ of initial temperature during a reversible change. If there is no exchange of heat in this process $(\Delta \mathrm{Q}=0)$ then identify the gas from the following options (Assuming the gases given in the options are ideal gases) :

The r.m.s. speed of oxygen molecules at 47 °C is equal to that of the hydrogen molecules kept at _________ °C. (Mass of oxygen molecule/mass of hydrogen molecule = 32/2)