The coefficients of thermal conductivity of copper,mercury,and glass are respectively $K_c, K_m$,and $K_g$ such that $K_c > K_m > K_g$. If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are $X_c, X_m$,and $X_g$,then:

Three rods of same dimensions have thermal conductivities $3K, 2K$ and $K$. They are arranged as shown with their ends at $100^{\circ}C, 50^{\circ}C$ and $0^{\circ}C$. The temperature of the junction is

$A$ body of length $1 \; m$ having a cross-sectional area of $0.75 \; m^2$ has heat flow through it at the rate of $6000 \; J/s$. Find the temperature difference if the thermal conductivity $K = 200 \; J \cdot m^{-1} \cdot s^{-1} \cdot K^{-1}$.

$A$ thermocol box has a total wall area (including the lid) of $1.0 \,m^2$ and wall thickness of $3 \,cm$. It is filled with ice at $0^{\circ} C$. If the average temperature outside the box is $30^{\circ} C$ throughout the day, the amount of ice that melts in one day is (Given: $K_{\text{thermocol}} = 0.03 \,W/mK$, $L_{\text{fusion(ice)}} = 3.00 \times 10^5 \,J/kg$) (in $\,kg$)

Heat is conducted across a composite block of two slabs of thickness $d$ and $2d$. Their thermal conductivities are $2k$ and $k$ respectively. All the heat entering the face $AB$ leaves from the face $CD$. The temperature in $^oC$ of the junction $EF$ of the two slabs is:

$A$ cylindrical rod has temperatures $\theta_1$ and $\theta_2$ at its ends. The rate of heat flow is $Q$. All the linear dimensions of the rod are doubled while keeping the temperatures constant. The new rate of flow of heat is