$1.56 \times 10^5 \ J$ of heat is conducted through a $2 \ m^2$ wall of $12 \ cm$ thickness in one hour. The temperature difference between the two sides of the wall is $20^{\circ} C$. The thermal conductivity of the material of the wall is (in $W \ m^{-1} \ K^{-1}$):

There are two identical vessels filled with equal amounts of ice. The vessels are made of different metals. If the ice melts in the two vessels in $20$ and $35$ minutes respectively,the ratio of the coefficients of thermal conductivity of the two metals 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.

Which of the following material properties is most suitable for a cooking utensil?

Three metal rods made of copper, brass, and steel, each with a cross-sectional area of $4 \,cm^2$, are joined as shown in the figure. Their lengths are $46 \,cm, 13 \,cm$, and $12 \,cm$ respectively. Their coefficients of thermal conductivity are $0.92, 0.26$, and $0.12$ respectively, all in $CGS$ units. The rods are thermally insulated from the surroundings except at the ends. The rate of flow of heat through the copper rod, in $cal \,s^{-1}$, is:

The temperature difference between the ends of two cylindrical rods $A$ and $B$ of the same material is $2: 3$. In steady state, the ratio of the rates of flow of heat through the rods $A$ and $B$ is $5: 9$. If the radii of the rods $A$ and $B$ are in the ratio $1: 2$, then the ratio of lengths of the rods $A$ and $B$ is