The temperature gradient in a rod of $0.5 m$ long is ${80^o}C/m$. If the temperature of hotter end of the rod is ${30^o}C$, then the temperature of the cooler end is ...... $^oC$

A slab consists of two parallel layers of two different materials of same thickness having thermal conductivities $K_1$ and $K_2$ . The equivalent conductivity of the combination is

A deep rectangular pond of surface area $A,$ containing water (denstity $=\rho,$ specific heat capactly $=s$ ), is located In a region where the outside air temperature is at a steady value of $-26^{\circ} {C}$. The thickness of the frozen ice layer In this pond, at a certaln Instant Is $x$.

Taking the thermal conductivity of Ice as ${K}$, and its specific latent heat of fusion as $L$, the rate of Increase of the thickness of ice layer, at this instant would be given by 

Two different rods $A$ and $B$ are kept as shown in figure. The ratio of thermal conductivities of $A$ and $B$ is

A metallic rod of cross-sectional area $9.0\,\,cm^2$ and length $0.54 \,\,m$, with the surface insulated to prevent heat loss, has one end immersed in boiling water and the other in ice-water mixture. The heat conducted through the rod melts the ice at the rate of $1 \,\,gm$ for every $33 \,\,sec$. The thermal conductivity of the rod is ....... $ Wm^{-1} K^{-1}$

The coefficients of thermal conductivity of copper, mercury and glass are respectively $Kc, Km$ and $Kg$ such that $Kc > Km > Kg$ . If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are $Xc, Xm$ and $Xg$ , then