The temperature difference between two sides of an iron plate,$1.8 \ cm$ thick is $9^{\circ} C$. Heat is transmitted through the plate at a rate of $10 \ kcal / (s \cdot m^2)$ at steady state. The thermal conductivity of iron is:

An ice box is used to keep food cool,having a surface area of $1 \, m^2$ and a thickness of $5.0 \, cm$. The thermal conductivity of the ice box material is $K = 0.01 \, J/(m \cdot s \cdot ^\circ C)$. The inside temperature is maintained at $0 \, ^\circ C$ and the outside temperature is $30 \, ^\circ C$. If the latent heat of fusion of ice is $334 \times 10^3 \, J/kg$,calculate the mass of ice that melts in one day.

If $4 \, kg$ of ice is inside a closed cubical thermocol box of side length $20 \, cm$ and wall thickness $4 \, cm$, then the mass of the ice remaining after $10 \, hours$ is nearly. (Given: Outside temperature $= 50^{\circ}C$, Thermal conductivity of thermocol $K = 0.01 \, Js^{-1}m^{-1\circ}C^{-1}$, Latent heat of fusion of ice $L = 335 \times 10^3 \, Jkg^{-1}$) (in $ \, kg$)

Three rods made of the same material and having the same cross-sectional area but different lengths $10 \ cm$,$20 \ cm$,and $30 \ cm$ are joined as shown. The temperature of the joint is ....... $^oC$.

Four rods with different radii $r$ and length $l$ are used to connect two heat reservoirs at different temperatures. Which one will conduct the most heat?

The temperature difference across two cylindrical rods $A$ and $B$ of the same material and same mass are $40^{\circ} C$ and $60^{\circ} C$ respectively. In steady state,if the rates of flow of heat through the rods $A$ and $B$ are in the ratio $3: 8$,the ratio of the lengths of the rods $A$ and $B$ is (in $: 3$)