Mud houses are cooler in summer and warmer in winter because

The ends $Q$ and $R$ of two thin wires,$PQ$ and $RS$,are soldered (joined) together. Initially,each of the wires has a length of $1 \,m$ at $10^{\circ} C$. Now,the end $P$ is maintained at $10^{\circ} C$,while the end $S$ is heated and maintained at $400^{\circ} C$. The system is thermally insulated from its surroundings. If the thermal conductivity of wire $PQ$ is twice that of the wire $RS$ and the coefficient of linear thermal expansion of $PQ$ is $1.2 \times 10^{-5} \,K^{-1}$,the change in length of the wire $PQ$ is (in $\,mm$)

$A$ slab of stone of area $0.36\, m^2$ and thickness $0.1\, m$ is exposed on the lower surface to steam at $100^{\circ} C$. $A$ block of ice at $0^{\circ} C$ rests on the upper surface of the slab. In one hour $4.8\, kg$ of ice is melted. The thermal conductivity of the slab is .......... $J/m/s/^{\circ} C$ (Given latent heat of fusion of ice $= 3.36 \times 10^5\, J/kg$)

Two ends of rods of length $L$ and radius $r$ of the same material are kept at the same temperature difference. Which of the following rods conducts the most heat?

$A$ 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 that of $B$. In thermal equilibrium,the temperature difference between the two ends is $36^{\circ}C$. Then the difference of temperature at the two surfaces of $A$ will be ....... $^{\circ}C$

$A$ long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length $x$ of the bar from its hot end is best described by which of the following figures?