The rate of heat conduction in the given two metal rods having the same length is found to be the same when the temperature difference between the ends is kept $30^{\circ} \mathrm{C}$ If the area of cross section of the first rod is $8 \times 10^{-2} \mathrm{~m}^2$ then what will be area of cross section of the second rod? [ Given that the ratio of the thermal conductivity of the first rod to that of the second rod is $1: 4$ ]

The heat required to increase the temperature of 4 moles of a mono-atomic ideal gas from $273^{\circ} \mathrm{C}$ to $473^{\circ} \mathrm{C}$ at constant volume is

Rods $A$ and $B$ have their lengths in the ratio $1: 2$. Their thermal conductivities are $K_1$ and $K_2$ respectively. The temperatures at the ends of each rod are $\mathrm{T}_1$ and $\mathrm{T}_2$. If the rate of flow of heat through the rods is equal, the ratio of area of cross section of $A$ to that of $B$ is

A monoatomic ideal gas, initially at temperature $T_1$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $\mathrm{T}_2$ by releasing the piston suddenly. If $L$ and $2 L$ are the lengths of the gas column before and after expansion respectively, then $\frac{T_1}{T_2}$ is