$A$ wall is made up of two layers $A$ and $B$ . The thickness of the two layers is the same, but materials are different. The thermal conductivity of $A$ is double than that of $B$ . In thermal equilibrium the temperature difference between the two ends is ${36^o}C$. Then the difference of temperature at the two surfaces of $A$ will be ....... $^oC$

In the Arctic region, hemispherical houses called Igloos are made of ice. It is possible to maintain a temperature inside an Igloo as high as $20^{\circ} C$ because

The temperature of hot and cold end of a $20cm$ long rod in thermal steady state are at ${100^o}C$ and ${20^o}C$ respectively. Temperature at the centre of the rod is...... $^oC$

An iron bar $\left(L_{1}=0.1\; m , A_{1}\right.$ $\left.=0.02 \;m ^{2}, K_{1}=79 \;W m ^{-1} K ^{-1}\right)$ and a brass bar $\left(L_{2}=0.1\; m , A_{2}=0.02\; m ^{2}\right.$ $K_{2}=109 \;Wm ^{-1} K ^{-1}$ are soldered end to end as shown in Figure. The free ends of the iron bar and brass bar are maintained at $373 \;K$ and $273\; K$ respectively. Obtain expressions for and hence compute

$(i)$ the temperature of the junction of the two bars,

$(ii)$ the equivalent thermal conductivity of the compound bar, and

$(iii)$ the heat current through the compound bar.

One end of a metal rod of length $1.0 m$ and area of cross section $100c{m^2}$ is maintained at ${100^o}C.$If the other end of the rod is maintained at ${0^o}C$, the quantity of heat transmitted through the rod per minute is (Coefficient of thermal conductivity of material of rod =$100W/m-K$)

Woollen clothes are used in winter season because woolen clothes