Two metal cubes $A$ and $B$ of the same size are arranged as shown in the figure. The ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. If the thermal conductivities of $A$ and $B$ are $300 \, W/m \, ^\circ C$ and $200 \, W/m \, ^\circ C$ respectively,find the temperature $t$ at the junction when the steady state is reached.

Two spheres made of different materials have radii in the ratio $2:1$ and wall thicknesses in the ratio $1:4$. They are completely filled with ice. If the time taken to melt the ice completely in the larger sphere is $25 \ min$ and in the smaller sphere is $16 \ min$,then the ratio of the thermal conductivities of the materials of the larger and smaller spheres is ..........

Two metal rods $1$ and $2$ of same lengths have same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$ and cross-sectional areas are $A_1$ and $A_2$,respectively. If the rate of heat conduction in rod $1$ is four times that in rod $2$,then:

The thickness of a metallic plate is $0.4 \ cm$. The temperature difference between its two surfaces is $20^{\circ}C$. The quantity of heat flowing per second is $50 \ \text{calories}$ through an area of $5 \ cm^2$. In the $CGS$ system,the coefficient of thermal conductivity is:

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity $2K$ while that in the middle has thermal conductivity $K$. The left end of the combination is maintained at temperature $3T$ and the right end at $T$. The rods are thermally insulated from outside. In steady state,the temperature at the left junction is $T_1$ and that at the right junction is $T_2$. The ratio $T_1 / T_2$ is

The two ends of a metal rod are maintained at temperatures $100 ^\circ C$ and $110 ^\circ C$. The rate of heat flow in the rod is found to be $4.0 \ J/s$. If the ends are maintained at temperatures $200 ^\circ C$ and $210 ^\circ C$,the rate of heat flow will be.... $J/s$