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 $K$)
$\frac{{K\pi {r_1}{r_2}\left( {{T_2} - {T_1}} \right)}}{L}$
$\frac{{K\pi {{\left( {{r_1} + {r_2}} \right)}^2}\left( {{T_2} - {T_1}} \right)}}{{4L}}$
$\frac{{K\pi {{\left( {{r_1} + {r_2}} \right)}^2}\left( {{T_2} - {T_1}} \right)}}{{L}}$
$\frac{{K\pi {{\left( {{r_1} + {r_2}} \right)}^2}\left( {{T_2} - {T_1}} \right)}}{{2L}}$
Three rods $AB, BC$ and $AC$ having thermal resistances of $10\, units, \,10 \,units$ and $20 \,units,$ respectively, are connected as shown in the figure. Ends $A$ and $C$ are maintained at constant temperatures of $100^o C$ and $0^o C,$ respectively. The rate at which the heat is crossing junction $B$ is ........ $ \mathrm{units}$
Two plates $A$ and $B$ have thermal conductivities $84\,Wm ^{-1}\,K ^{-1}$ and $126\,Wm ^{-1}\,K ^{-1}$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of $A$ and $B$ are kept at $100^{\circ}\,C$ and $0{ }^{\circ}\,C$ respectively, then the temperature of the surface of contact in steady state is $..........\,{ }^{\circ} C$.
Mud houses are cooler in summer and warmer in winter because
A metallic prong consists of $4$ rods made of the same material, cross-sections and same lengths as shown below. The three forked ends are kept at $100^{\circ} C$ and the handle end is at $0^{\circ} C$. The temperature of the junction is ............. $^{\circ} C$
On a cold morning, a metal surface will feel colder to touch than a wooden surface because