Four rods of same material and having the same cross section and length have been joined, as shown. The temperature of junction of four rods will be…….. $^oC$

The thermal conductivity of a material in $CGS$ system is $0.4$ . In steady state, the rate of flow of heat $10 cal/sec-cm2$ , then the thermal gradient will be ……. $^oC/cm$

Three rods of the same dimensions have thermal conductivities $3k, 2k$ and $k$. They are arranged as shown, with their ends at $100\,^oC, 50\,^oC$ and $0\,^oC$. The temperature of their junction 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.

Surface of the lake is at $2°C$ . Find the temperature of the bottom of the lake….. $^oC$