$A$ cylinder of radius $R$ made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity $K_2$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

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.

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

The power radiated by a black body is $P$ and it radiates maximum energy around the wavelength $\lambda_0$. Now the temperature of the black body is changed so that it radiates maximum energy around wavelength $\left(\frac{\lambda_0}{2}\right)$. The power radiated by it will now increase by a factor of

Power radiated by a black body at temperature $T_1$ is $P$ and it radiates maximum energy at a wavelength $\lambda_1$. If the temperature of the black body is changed from $T_1$ to $T_2$, it radiates maximum energy at a wavelength $\frac{\lambda_1}{2}$. The power radiated at $T_2$ is (in $P$)

Fill in the blanks:
$(a)$ $0.49 \frac{\text{cal}}{\text{cm} \cdot \text{K} \cdot \text{s}} = \dots \frac{\text{J}}{\text{m} \cdot \text{K} \cdot \text{s}}$
$(b)$ If the rate of emission of heat of a substance is less than its rate of absorption,then its temperature $\dots$.
$(c)$ The rate of emission of heat of a substance is directly proportional to $\dots$ of temperature of it and surroundings.