Two materials having coefficients of thermal conductivity $3K$ and $K$ and thickness $d$ and $3d$, respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are  $\theta_2$ and $\theta_1$ respectively  $\left( {\theta _2} > {\theta _1} \right)$ . The temperature at the interface 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....... $^oC$

Woollen clothes are used in winter season because woolen clothes

A copper rod $2\,m$ long has a circular cross-section of radius $1\, cm$. One end is kept  at $100^o\,C$ and the other at $0^o\,C$ and the surface is covered by nonconducting material to check the heat losses through the surface. The thermal  resistance of the bar in degree kelvin per watt is (Take thermal conductivity $K = 401\, W/m-K$ of copper):-

As per the given figure, two plates $A$ and $B$ of thermal conductivity $K$ and $2 K$ are joined together to form a compound plate. The thickness of plates are $4.0 \,cm$ and $2.5 \,cm$ respectively and the area of cross-section is $120 \,cm ^{2}$ for each plate. The equivalent thermal conductivity of the compound plate is $\left(1+\frac{5}{\alpha}\right) K$, then the value of $\alpha$ will be_______

Surface of the lake is at $2^{\circ} C$. The temperature of the bottom of the lake is ....... $^{\circ} C$