Bottom of a lake is at $0^{\circ} C$ and atmospheric temperature is $-20^{\circ} C$. If $1 cm$ ice is formed on the surface in $24 \,h$, then time taken to form next $1 \,cm$ of ice is ......... $h$

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 ....... $^oC/cm$

Four rods of same material and having the same cross section and length have been joined, as shown. The temperature of the junction of four rods will be ............... $^{\circ} C$

In the following figure, two insulating sheets with thermal resistances $R$ and $3R$ as shown in figure. The temperature $\theta$ is ...... $^oC$

Two cylinders $P$ and $Q$ have the same length and diameter and are made of different materials having thermal conductivities in the ratio $2 : 3$ . These two cylinders are combined to make a cylinder. One end of $P$ is kept at $100°C$  and another end of $Q$ at $0°C$ . The temperature at the interface of $P$ and $Q$ is ...... $^oC$

Four rods of silver, copper, brass and wood are of same shape. They are heated together after wrapping a paper on it, the paper will burn first on