Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20 \text{ minutes}$ and $30 \text{ minutes}$ respectively. The ratio of their thermal conductivities will be

Two spheres of different materials,one with double the radius and one-fourth wall thickness of the other,are filled with ice. If the time taken for complete melting of ice in the large radius sphere is $25 \ minutes$ and that for the smaller one is $16 \ minutes$,the ratio of thermal conductivities of the materials of the larger sphere to the smaller sphere is:

Three rods each of length $l$ and cross-sectional area $A$ are joined in series between two heat reservoirs as shown in the figure. Their thermal conductivities are $2K$,$K$,and $\frac{K}{2}$,respectively. Assuming that the conductors are insulated from the surroundings,the temperatures $T_1$ and $T_2$ of the junctions in the steady-state condition are,respectively:

In an $Ingen-Hauz$ experiment,the wax melts on two rods up to lengths of $10 \ cm$ and $25 \ cm$ respectively. If the two rods are made of different materials,what is the ratio of their thermal conductivities?

Three rods of same dimensions have thermal conductivities $3K, 2K$ and $K$. They are arranged as shown in the figure. In the steady state,the temperature of the junction $P$ is:

Two identical long bars $A$ and $B$ made of different materials are coated with wax and have one end immersed in a hot oil bath. When the steady state is reached,the lengths for which the wax melts are $l_A$ and $l_B$. If $k_A$ and $k_B$ are the thermal conductivities of the materials,then: