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

Which of the following statements is/are $CORRECT$?
$(i)$ $A$ body with large reflectivity is a poor emitter.
$(ii)$ $A$ brass tumbler feels much colder than a wooden tray on a chilly day.
$(iii)$ The Earth without its atmosphere would be inhospitably cold.
$(iv)$ Heating systems based on the circulation of steam are more efficient in warming a building than those based on the circulation of hot water.

Three rods of Copper,Brass,and Steel are welded together to form a $Y$ shaped structure. The area of cross-section of each rod is $4 \ cm^2$. The end of the copper rod is maintained at $100^\circ C$,whereas the ends of the brass and steel rods are kept at $0^\circ C$. The lengths of the copper,brass,and steel rods are $46 \ cm$,$13 \ cm$,and $12 \ cm$ respectively. The rods are thermally insulated from the surroundings except at the ends. The thermal conductivities of copper,brass,and steel are $0.92$,$0.26$,and $0.12 \ CGS$ units respectively. The rate of heat flow through the copper rod is ....... $cal \ s^{-1}$.

$A$ 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?

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

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