The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ and kept at temperatures $T_1$ and $T_2$, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to
$\frac{{{r_1}\,{r_2}}}{{({r_1} - {r_2})}}$
$({r_2} - {r_1})$
$({r_2} - {r_1})({r_1}\,{r_2})$
$In \left( {\frac{{{r_2}}}{{{r_1}}}} \right)$
Two walls of thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ are in contact. In the steady state, if the temperatures at the outer surfaces are ${T_1}$ and ${T_2}$, the temperature at the common wall is
In a steady state of thermal conduction, temperature of the ends $A$ and $B$ of a $20\, cm$ long rod are ${100^o}C$ and ${0^o}C$ respectively. What will be the temperature of the rod at a point at a distance of $6$ cm from the end $A$ of the rod....... $^oC$
A copper pipe of length $10 \,m$ carries steam at temperature $110^{\circ} C$. The outer surface of the pipe is maintained at a temperature $10^{\circ} C$. The inner and outer radii of the pipe are $2 \,cm$ and $4 \,cm$, respectively. The thermal conductivity of copper is $0.38 kW / m /{ }^{\circ} C$. In the steady state, the rate at which heat flows radially outward through the pipe is closest to ............. $\,kW$
The coefficient of thermal conductivity depends upon
A large cylindrical rod of length $L$ is made by joining two identical rods of copper and steel of length $(\frac {L}{2})$ each . The rods are completely insulated from the surroundings. If the free end of copper rod is maintained at $100\,^oC$ and that of steel at $0\,^oC$ then the temperature of junction is........$^oC$ (Thermal conductivity of copper is $9\,times$ that of steel)