$A$ body of length $1 \; m$ having a cross-sectional area of $0.75 \; m^2$ has heat flow through it at the rate of $6000 \; J/s$. Find the temperature difference if the thermal conductivity $K = 200 \; J \cdot m^{-1} \cdot s^{-1} \cdot K^{-1}$.

The thermal conductivity of copper is $9$ times that of steel. Find the temperature of the junction of copper and steel in the composite rod as shown in the figure (in $^oC$).

$A$ rod $A$ of length $40\, cm$ has a temperature difference of $80^\circ C$ at its two ends. Another rod $B$ of length $60\, cm$ has a temperature difference of $90^\circ C$ at its ends. Both rods have the same area of cross-section. If the rate of flow of heat is the same for both,then the ratio of their thermal conductivities $(K_A : K_B)$ will be:

If the thermal conductivity of copper is $9$ times that of steel,what will be the temperature of the junction in $^oC$?

Heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio $1:2$ and their lengths are in the ratio $2:1$. If the temperature difference between their ends is the same,then the ratio of the amounts of heat conducted through per unit time will be

One end of a copper rod of uniform cross-section and of length $3.1 \ m$ is kept in contact with ice at $0^{\circ}C$ and the other end with water at $100^{\circ}C$. At what point along its length should a temperature of $200^{\circ}C$ be maintained so that in steady state,the mass of ice melting is equal to the mass of steam produced in the same interval of time? Assume that the whole system is insulated from the surroundings. Latent heat of fusion of ice and vaporisation of water are $80 \ cal/g$ and $540 \ cal/g$ respectively.