One end of a copper rod of uniform cross-section and of length $3.1$ m is kept in contact with ice and the other end with water at $100°C $ . At what point along it's length should a temperature of $200°C$ be maintained so that in steady state, the mass of ice melting be equal to that of the 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 $80 cal/gm$ and $540$ cal/gm respectively

When thermal conductivity is said to be constant ?

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 $'A'$  ....... $^oC$ 

A wall consists of alternating blocks of length $d$ and coefficient of thermal conductivity $K_{1}$ and $K_{2}$ respectively as shown in figure. The cross sectional area of the blocks are the same. The equivalent coefficient of thermal conductivity of the wall between left and right is

If the ratio of coefficient of thermal conductivity of silver and copper is $10 : 9$ , then the ratio of the lengths upto which wax will melt in Ingen Hausz experiment will be

Two metal cubes $A$ and $B$ of same size are arranged as shown in the figure. The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of $A$ and $B$ are $300\;W/m{\;^o}C$ and $200\;W/m{\;^o}C$, respectively. After steady state is reached, the temperature of the interface will be...... $^oC$