The dimensions of $\sigma b^4$, where $\sigma$ is Stefan's constant and $b$ is Wien's constant, are:

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.

$A$ wall with a cavity consists of two layers of brick separated by a layer of air. All three layers have the same thickness,and the thermal conductivity of the brick is much greater than that of air. The left layer is at a higher temperature than the right layer,and a steady-state condition exists. Which of the following graphs correctly predicts the variation of temperature $T$ with distance $d$ inside the cavity?

In the variable state,the rate of flow of heat is controlled by

$A$ black body radiates maximum energy at wavelength $\lambda$ at temperature $T_1$ and its emissive power is $E$. When the temperature of the body is changed to $T_2$, it radiates maximum energy at wavelength $\frac{2\lambda}{3}$, then the emissive power will become

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?