In a closed room,heat transfer takes place by

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 $2$?

$A$ thin piece of thermal conductor of constant thermal conductivity,insulated on the lateral sides,connects two reservoirs which are maintained at temperatures $T_{1}$ and $T_{2}$ as shown in the figure. Assuming that the system is in a steady state,which of the following plots best represents the dependence of the rate of change of entropy on the ratio $T_{1} / T_{2}$?

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?

Explain why:
$(a)$ a body with large reflectivity is a poor emitter.
$(b)$ a brass tumbler feels much colder than a wooden tray on a chilly day.
$(c)$ an optical pyrometer (for measuring high temperatures) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open,but gives a correct value for the temperature when the same piece is in the furnace.
$(d)$ the earth without its atmosphere would be inhospitably cold.
$(e)$ heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water.

The power radiated by a black body is $P$ and it radiates maximum energy around the wavelength $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy around wavelength $\frac{3}{4}\lambda_0$,the power radiated by it will increase by a factor of