A slab of stone of area $0.36\;m ^2$ and thickness $0.1 \;m$ is exposed on the lower surface to steam at $100^{\circ} C$. A block of ice at $0^{\circ} C$ rests on the upper surface of the slab. In one hour $4.8\; kg$ of ice is melted. The thermal conductivity of slab is .......... $J / m / s /{ }^{\circ} C$ (Given latent heat of fusion of ice $=3.36 \times 10^5\; J kg ^{-1}$)

A partition wall has two layers $A$ and $B$ in contact, each made of a different material. They have the same thickness but the thermal conductivity of layer $A$ is twice that of layer $B$. If the steady state temperature difference across the wall is $60K$, then the corresponding difference across the layer $A$ is ....... $K$

The temperature gradient in a rod of $0.5 m$ long is ${80^o}C/m$. If the temperature of hotter end of the rod is ${30^o}C$, then the temperature of the cooler end is ...... $^oC$

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 ........... $^{\circ} C$

Two rods one made of copper and other made of steel of the same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are $385\,J\,s ^{-1}\,K ^{-1}\,m ^{-1}$ and $50\,J\,s ^{-1}\,K ^{-1}\,m ^{-1}$ respectively. The free ends of copper and steel are held at $100^{\circ}\,C$ and $0^{\circ}\,C$ respectively. The temperature at the junction is, nearly $.......^{\circ}\,C$

On heating one end of a rod, the temperature of whole rod will be uniform when