The lengths and radii of two rods made of same material are in the ratios $1 : 2$ and $2 : 3$ respectively. If the temperature difference between the ends for the two rods be the same, then in the steady state, the amount of heat flowing per second through them will be in the ratio

Figure shows three different arrangements of materials $1, 2$ and $3$ to form a wall. Thermal conductivities are $k_1 > k_2 > k_3$ . The left side of the wall is $20\,^oC$ higher than the right side. Temperature difference $\Delta T$ across the material $1$ has following relation in three cases

An ice cube of dimensions $60\,cm \times 50\,cm \times 20\,cm$ is placed in an insulation box of wall thickness $1\,cm$. The box keeping the ice cube at $0^{\circ}\,C$ of temperature is brought to a room of temperature $40^{\circ}\,C$. The rate of melting of ice is approximately. (Latent heat of fusion of ice is $3.4 \times 10^{5}\,J\,kg ^{-1}$ and thermal conducting of insulation wall is $0.05\,Wm ^{-10} C ^{-1}$ )

Two plates $A$ and $B$ have thermal conductivities $84\,Wm ^{-1}\,K ^{-1}$ and $126\,Wm ^{-1}\,K ^{-1}$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of $A$ and $B$ are kept at $100^{\circ}\,C$ and $0{ }^{\circ}\,C$ respectively, then the temperature of the surface of contact in steady state is $..........\,{ }^{\circ} C$.

Find Temperature difference between $B$ and $C$ ? (All rods are identical)

Twelve conducting rods form the riders of a uniform cube of side $'l'.$ If in steady state, $B$ and $H$ ends of the rod are at $100^o C$ and $0^o C$. Find the temperature of the junction $'A'$  ....... $^oC$