Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The points $A$ and $B$ are maintained at different temperature. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross section of the straight rod in a given time is

Two bars of thermal conductivities $K$ and $3K$ and lengths $1\,\, cm$ and $2\,\, cm$ respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is $0\,^oC$ and $100\,^oC$ respectively (see figure), then the temperature $\varphi $ of the interface is……… $^oC$

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 ($L = 80 cal/g, Kicc = 0.004 Erg/s-k, dice = 0.92 g cm^{-3}$)

A metal rod of length $2\, m$ has cross-sectional areas $2A$ and $A$ as shown in the following figure. The two ends are maintained at temperatures $100\,^oC$ and $70\,^oC$. The temperature of middle point $C$ is …….. $^oC$

A rod $C D$ of thermal resistance $10.0\; {KW}^{-1}$ is joined at the middle of an identical rod ${AB}$ as shown in figure, The end $A, B$ and $D$ are maintained at $200^{\circ} {C}, 100^{\circ} {C}$ and $125^{\circ} {C}$ respectively. The heat current in ${CD}$ is ${P}$ watt. The value of ${P}$ is … .