A hollow sphere of inner radius $R$ and outer radius $2R$ is made of a material of thermal conductivity $K$. It is surrounded by another hollow sphere of inner radius $2R$ and outer radius $3R$ made of same material of thermal conductivity $K$. The inside of smaller sphere is maintained at $0^o C$ and the outside of bigger sphere at $100^o C$. The system is in steady state. The temperature of the interface will be ........ $^oC$

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

The heat is flowing through a rod of length $50 cm$ and area of cross-section $5c{m^2}$. Its ends are respectively at ${25^o}C$ and ${125^o}C$. The coefficient of thermal conductivity of the material of the rod is $0.092 kcal/m×s×^\circ C$. The temperature gradient in the rod is

Three rods of the same dimension have thermal conductivities $3K$ , $2K$ and $K$ . They are arranged as shown in fig. Given below, with their ends at $100^oC, 50^oC $and $20^oC$. The temperature of their junction is ......... $^oC$

$Assertion :$ Two thin blankets put together are warmer than a single blanket of double the thickness.
$Reason :$ Thickness increases because of air layer enclosed between the two blankets.

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