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 ice in the large radius one is $25$ minutes and that for smaller one is $16$ minutes, the ratio of thermal conductivities of the materials of larger sphere to the smaller sphere is

One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$ . The rod is composed of two sections of length $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two section is

Find effective thermal resistance between $A$ & $B$ of cube made up of $12$ rods of same dimensions and shown given thermal conductivity. [ $l =$ length of rod, $a =$ cross section area of rod]

The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_1$ and $T_2 (T_1 > T_2)$. The rate of heat transfer,$\frac{ dQ }{dt}$, through the rod in a steady state is given by

An ice box used for keeping eatable cold has a total wall area of $1\;metr{e^2}$ and a wall thickness of $5.0cm$. The thermal conductivity of the ice box is $K = 0.01\;joule/metre{ - ^o}C$. It is filled with ice at ${0^o}C$ along with eatables on a day when the temperature is $30°C$ . The latent heat of fusion of ice is $334 \times {10^3}joules/kg$. The amount of ice melted in one day is ........ $gms$ ($1day = 86,400\;\sec onds$) 

One likes to sit under sunshine in winter season, because