Three rods of Copper, Brass and Steel are welded together to form a Y-shaped structure. Area of cross-section of each rod is $4 {\mathrm{cm}}^2$. End of copper rod is maintained at $100°\mathrm{C}$. Where as ends of brass and steel are kept at $0°\mathrm{C}$. Lengths of the copper, brass and steel rods are $46, 13$and $12 \mathrm{cms}$ respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are $0.92, 0.26$ and $0.12$ CGS units respectively. Rate of heat flow through copper rod is :

The temperature difference of $120 °\mathrm{C}$ is maintained between two ends of a uniform rod $AB$ of length $2L$. Another bent rod $PQ$, of the same cross-section as $AB$ and length $\frac{3L}{2}$, is connected across $AB$ (see figure). In steady-state, the temperature difference between $P$ and $Q$ will be close to

A metallic sphere having radius $0.08 \mathrm{m}$ and mass $m=10 \mathrm{kg}$ is heated to a temperature of $227°\mathrm{C}$ and suspended inside a box whose walls are at a temperature of $27°\mathrm{C}$. The maximum rate at which its temperature will fall is :

(Take $e= 1$, Stefan’s constant $\mathrm{\sigma }= 5.8 \mathrm{x} {10}^{-8} \mathrm{W} {\mathrm{m}}^{-2} {\mathrm{K}}^{-4}$and specific heat of the metal $s= 90 \mathrm{cal} {\mathrm{kg}}^{-1}{\mathrm{deg}}^{-1},\mathit{ }\mathrm{J} = 4.2 \mathrm{Joules} {\mathrm{Calorie}}^{-1}$)