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

Two rectangular blocks, having identical dimensions, can be arranged either in the configuration $1$ or in configuration $2$ as shown in the figure. One of the blocks has thermal conductivity $K$ and the other $2K$. The temperature difference between the ends along the $x$ -axis is the same in both the configurations. It takes $9$ $\mathrm{s}$ to transport a certain amount of heat from the hot end to the cold end in the configuration $1$. The time to transport the same amount of heat in the configuration $2$ is

The figure shows the temperatures at four faces of a composite slab consisting of four materials $S_1,S_2,S_3$ and $S_4$ of identical thickness, through which the heat transfer is steady. Arrange the materials according to their thermal conductivities in decreasing order.

Three rods of the same dimensions are arranged as shown in the figure, they have thermal conductivities $K_1,K_2$ and $K_3$. The points $P$ and $Q$ are maintained at different temperatures for the heat to flow at the same rate along $PRQ$ and $PQ$

$A,B$ and $C$ are three identical conductors but made from different materials. They are kept in contact as shown. Their thermal conductivities are $K, 2K$ and $\frac{K}{2}$ respectively. The free end of $A$ is at $100°\mathrm{C}$ and the free end of $C$ is at $0°\mathrm{C}$. During steady-state, the temperature of the junction of $A$ and $B$ is nearly

Two spherical black bodies of radii $r_1$ and $r_2$ and with surface temperatures $T_1$ and $T_2$ respectively, radiate the same power. Then, the ratio of $r_1$ and $r_2$ will be