A composite block is made of slabs$A, B, C, D$ and $E$ of different thermal conductivities (given in terms of a constant, $K$) and sizes (given in terms of length, $L$) as shown in the figure. All slabs are of same width. Heat $Q$ flows only from left to right through the blocks. Then in steady state

 

Two rectangular blocks, having identical dimensions, can be arranged either in configuration $\mathrm{I}$ or in configuration $\mathrm{II}$ as shown in the figure, on 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 $\mathrm{I}$. The time to transport the same amount of heat in the configuration $\mathrm{II}$ is:

Parallel rays of light of intensity, $I=912 \mathrm{W} {\mathrm{m}}^{-1}$ are incident on a spherical blackbody kept in surroundings of temperature $300 \mathrm{K}$. Take Stefan-Boltzmann's constant, $\sigma =5.7\times {10}^{-8} \mathrm{W} {\mathrm{m}}^{-2} {\mathrm{K}}^{-4}$ and assume that the energy exchange with the surroundings is only through radiation. The final steady-state temperature of the blackbody is close to,

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T_1 = 300 \mathrm{K},$ and $T_{2 }= 100 \mathrm{K}$  as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are $K_1$ and $K_2$ respectively. If the temperature at the junction of the two cylinders in the steady state is $200 \mathrm{K}$, then $\frac{{\mathit{K}}_{\mathit{1}}}{{\mathit{K}}_{\mathit{2}}}=$__________.

Assuming the sun to be a spherical body of radius $R$ at a temperature of $T \mathrm{K}$, evaluate the total radiant power, incident on the earth, at a distance $r$ from the sun:

(radius of earth is $r_0$)

One end of a thermally insulated rod is kept at a temperature $T_{1 }$and the other at $T_2$. The rod is composed of two sections of lengths $L_1$ and $L_{2 }$and thermal conductivities $k_1$ and $k_2$ respectively. The temperature at the interface of the sections is