Wires $A$ and $B$ have identical lengths and have circular cross-sections. The radius of $A$ is twice the radius of $B$ $i.e.$ ${r_A} = 2{r_B}$. For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by

Three rods of identical area of cross-section and made from the same metal form the sides of an isosceles triangle $ABC$, right angled at $B$. The points $A$ and $B$ are maintained at temperatures $T$ and $\sqrt 2 T$ respectively. In the steady state the temperature of the point C is ${T_C}$. Assuming that only heat conduction takes place, $\frac{{{T_C}}}{T}$ is equal to

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 ........ $gms$ ($1day = 86,400\;\sec onds$) 

In Searle's method for finding conductivity of metals, the temperature gradient along the bar

Two rods of same length and material transfer a given amount of heat in $12$ seconds, when they are joined end to end. But when they are joined lengthwise, then they will transfer same heat in same conditions in ....... $\sec$

Four rods of silver, copper, brass and wood are of same shape. They are heated together after wrapping a paper on it, the paper will burn first on