Give definition, unit and dimensional formula of thermal conductivity.

Which of the following circular rods. (given radius $ r$ and length $l$ ) each made of the same material as whose ends are maintained at the same temperature will conduct most heat

One end of a copper rod of length $1.0\;m$ and area of cross-section ${10^{ – 3}}$ is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is $92\;cal/m{\rm{ – }}s{{\rm{ – }}^o}C$ and the latent heat of ice is $8 \times {10^4}cal/kg$, then the amount of ice which will melt in one minute is

An iron bar $\left(L_{1}=0.1\; m , A_{1}\right.$ $\left.=0.02 \;m ^{2}, K_{1}=79 \;W m ^{-1} K ^{-1}\right)$ and a brass bar $\left(L_{2}=0.1\; m , A_{2}=0.02\; m ^{2}\right.$ $K_{2}=109 \;Wm ^{-1} K ^{-1}$ are soldered end to end as shown in Figure. The free ends of the iron bar and brass bar are maintained at $373 \;K$ and $273\; K$ respectively. Obtain expressions for and hence compute

$(i)$ the temperature of the junction of the two bars,

$(ii)$ the equivalent thermal conductivity of the compound bar, and

$(iii)$ the heat current through the compound bar.

The dimensions of thermal resistance are