A cylindrical rod having temperature ${T_1}$ and ${T_2}$ at its ends. The rate of flow of heat is ${Q_1}$ $cal/sec$. If all the linear dimensions are doubled keeping temperature constant then rate of flow of heat ${Q_2}$ will be

Two rods, one made of copper and the other steel of the same length and cross-sectional area are joined together. The thermal conductivity of copper is $385 \,Js ^{-1} m ^{-1} K ^{-1}$ and steel is $50 \,Js ^{-1} m ^{-1} K ^{-1}$. If the copper end is held at $100^{\circ} C$ and the steel end is held at $0^{\circ} C$, the junction temperature is ……….. $C$ (Assuming no other heat losses)

In Searle's method for finding conductivity of metals, the temperature gradient along the bar

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 

There is formation of layer of snow $x\,cm$ thick on water, when the temperature of air is $ – {\theta ^o}C$ (less than freezing point). The thickness of layer increases from $x$ to $y$ in the time $t$, then the value of $t$is given by