The rate of heat flow through the cross-section of the rod shown in figure is ($T_2 > T_1$ and thermal conductivity of the material of the rod is $K$)
$\frac{{K\pi {r_1}{r_2}\left( {{T_2} - {T_1}} \right)}}{L}$
$\frac{{K\pi {{\left( {{r_1} + {r_2}} \right)}^2}\left( {{T_2} - {T_1}} \right)}}{{4L}}$
$\frac{{K\pi {{\left( {{r_1} + {r_2}} \right)}^2}\left( {{T_2} - {T_1}} \right)}}{{L}}$
$\frac{{K\pi {{\left( {{r_1} + {r_2}} \right)}^2}\left( {{T_2} - {T_1}} \right)}}{{2L}}$
Two bars of thermal conductivities $K$ and $3K$ and lengths $1\,\, cm$ and $2\,\, cm$ respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is $0\,^oC$ and $100\,^oC$ respectively (see figure), then the temperature $\varphi $ of the interface is......... $^oC$
$A$ wall has two layers $A$ and $B$ made of different materials. The thickness of both the layers is the same. The thermal conductivity of $A$ and $B$ are $K_A$ and $K_B$ such that $K_A = 3K_B$. The temperature across the wall is $20°C$ . In thermal equilibrium
A slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio $1 : 4$ . If the free face of brass is at ${100^o}C$ and that of copper at $0^\circ C $, the temperature of interface is ........ $^oC$
Two cylinders $P$ and $Q$ have the same length and diameter and are made of different materials having thermal conductivities in the ratio $2 : 3$ . These two cylinders are combined to make a cylinder. One end of $P$ is kept at $100°C$ and another end of $Q$ at $0°C$ . The temperature at the interface of $P$ and $Q$ is ...... $^oC$
In the Arctic region, hemispherical houses called Igloos are made of ice. It is possible to maintain a temperature inside an Igloo as high as $20^{\circ} C$ because