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........ $^oC$

Figure shows three different arrangements of materials $1, 2$ and $3$ to form a wall. Thermal conductivities are $k_1 > k_2 > k_3$ . The left side of the wall is $20\,^oC$ higher than the right side. Temperature difference $\Delta T$ across the material $1$ has following relation in three cases

A rod of length $L$ and uniform cross-sectional area has varying thermal conductivity which changes linearly from $2K$ at endAto $K$ at the other end $B$. The endsA and $B$ of the rod are maintained at constant temperature $100^o C$ and $0^o C$, respectively. At steady state, the graph of temperature : $T = T(x)$ where $x =$ distance from end $A$ will be

A $5cm$ thick ice block is there on the surface of water in a lake. The temperature of air is $-10°C$ ; how much time it will take to double the thickness of the block ......  hour ($L = 80 cal/g, Kicc = 0.004 Erg/s-k, dice = 0.92 g cm^{-3}$)

If $K_{1}$ and $K_{2}$ are the thermal conductivities $L_{1}$ and $L _{2}$ are the lengths and $A _{1}$ and $A _{2}$ are the cross sectional areas of steel and copper rods respectively such that $\frac{K_{2}}{K_{1}}=9, \frac{A_{1}}{A_{2}}=2, \frac{L_{1}}{L_{2}}=2$.

Then, for the arrangement as shown in the figure. The value of temperature $T$ of the steel - copper junction in the steady state will be ........... $^{\circ} C$

The three rods shown in figure have identical dimensions. Heat flows from the hot end at a rate of $40 \,W$ in the arrangement $(a)$. Find the rates of heat flow when the rods are joined as in arrangement $(b)$ is ......... $W$ (Assume $K_al=200 \,W / m ^{\circ} C$ and $\left.K_{c u}=400 \,W / m ^{\circ} C \right)$