A cylindrical steel rod of length $0.10 \,m$ and thermal conductivity $50 \,Wm ^{-1} K ^{-1}$ is welded end to end to copper rod of thermal conductivity $400 \,Wm ^{-1} K ^{-1}$ and of the same area of cross-section but $0.20 \,m$ long. The free end of the steel rod is maintained at $100^{\circ} C$ and that of the copper rod at $0^{\circ} C$. Assuming that the rods are perfectly insulated from the surrounding, the temperature at the junction of the two rods is ................... $^{\circ} C$

When thermal conductivity is said to be constant ?

A heat source at $T = 10^3\, K$ is connected to another heat reservoir at $T = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, WK^{-1}\, m^{-1}$, the energy flux through it in the steady state is ........... $Wm^{-2}$

There is formation of layer of snow $x\,cm$ thick on water, when the temperature of air is $ - {\theta ^o}C$ (less than freezing point). The thickness of layer increases from $x$ to $y$ in the time $t$, then the value of $t$is given by

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

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20$ minutes and $40$ minutes respectively. The ratio of thermal conductivities of the materials is