Two rods (one semi-circular and other straight) of the same material and of the same cross-sectional area are joined as shown in the figure. The points $A$ and $B$ are maintained at different temperatures. The ratio of the heat transferred through a cross-section of the semi-circular rod to the heat transferred through a cross-section of the straight rod in a given time is

Three identical rods $AB$,$CD$ and $PQ$ are joined as shown. $P$ and $Q$ are midpoints of $AB$ and $CD$ respectively. Ends $A, B, C$ and $D$ are maintained at $0^{\circ} C, 100^{\circ} C, 30^{\circ} C$ and $60^{\circ} C$ respectively. The direction of heat flow in $PQ$ is

If heat conduction in Figure $1$ takes $12 \, sec$,how much time (in $sec$) will it take for the same amount of heat to be conducted in Figure $2$?

Three rods of the same dimension have thermal conductivities $3K$,$2K$,and $K$. They are arranged as shown in the figure,with their ends at $100^oC$,$50^oC$,and $20^oC$. The temperature of their junction is ......... $^oC$.

Three discs $A, B$ and $C$ having radii $2\; m, 4\; m,$ and $6\; m$ respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are $300\; nm, 400\; nm$ and $500\; nm$ respectively. The power radiated by them are $Q_A, Q_B$ and $Q_C$ respectively. Which of the following is true?

Heat loss takes place from a body maintained at a temperature of $400^{\circ} C$ to the surrounding air at $30^{\circ} C$ by convection and to the surrounding surfaces at $30^{\circ} C$ by radiation. The Newton's cooling coefficient is $20 \ W / m^2 \ K$ and the Stefan-Boltzmann constant is $5.67 \times 10^{-8} \ W / m^2 \ K^4$. If the rate of heat loss by convection is equal to the rate of heat loss by radiation,the emissivity of the body surface is