Exercise-2

The solar constant for the earth is $\Sigma .$ The surface temperature of the sun is $T \mathrm{K}.$ The sun subtends an angle $\theta$ at the earth

Temperature of black body is $3000 \mathrm{K}$ when black body cools, then change in wevelength $\mathrm{\Delta }\lambda =9$ micron corresponding to maximum energy density. Now temperature of black body is :-

Two Plates of equal areas are placed in contact with each other. Their thickness are $2 \mathrm{cm}$ and $3 \mathrm{cm}$ respectively. Temperature of external surface of first plate is $-25°\mathrm{C}$ and that of external surface of second plate is $25°\mathrm{C}$ What will be temperature of contact surface if the plates :-
(i) Are of same material
(ii) Have thermal Conductivity in ratio $2: 3$.

Two identical square rods of metal are welded end to end as shown in figure (a) $20$ calories of heat flows. through it in $4$ minutes. If the rods are welded as shown in figure (b), the same amount of heat will flow through the rods in :-

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 $PQ$

The temperature of the two outer surface of a composite slab, consisting of two materials having coefficient of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x$, respectively are $T_2$ and $T_2$ $\left(T_2>T_1\right)$. The rate of heat transfer through the slab, in a steady state is $\left(\frac{A\left(T_2-T_1\right)K}{x}\right)f$, with $f$ equals to

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ and kept at temperatures $T_1$ and $T_2$ respectively. The radial rate of flow of heat in a substance between the two concentric sphere is proportional to

A closed cubical box made of perfectly insulating material has walls of thickness, $8 \mathrm{cm}$, and the only way for the heat to enter or leave the box is through the two solid, metallic plugs, $A \& B$ each of cross-sectional area, $12{ \mathrm{cm}}^2$ and length, $8 \mathrm{cm}$ fixed in the opposite walls of the box as shown in the given figure. The outer surface, $A$ is kept at $100°\mathrm{C}$ while the outer surface, $B$ of other plugs, is kept at, $4°\mathrm{C}$. $K$ of the material of the plugs is, $0.5 \mathrm{cal} {\mathrm{s}}^{-1}\left(°{\mathrm{C}}^{-1}\right)$. A source of energy generating, $36 \mathrm{cal} {\mathrm{s}}^{-1}$ is enclosed inside the box. Find the equilibrium temperature of the inner surface of the box assuming that it is the same at all points on the inner surface.