An ice box used for keeping eatable cold has a total wall area of $1\;metr{e^2}$ and a wall thickness of $5.0cm$. The thermal conductivity of the ice box is $K = 0.01\;joule/metre{ – ^o}C$. It is filled with ice at ${0^o}C$ along with eatables on a day when the temperature is $30°C$ . The latent heat of fusion of ice is $334 \times {10^3}joules/kg$. The amount of ice melted in one day is …….. $gms$ ($1day = 86,400\;\sec onds$) 

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 

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):-

The ratio of thermal conductivity of two rods of different material is $5 : 4$ . The two rods of same area of cross-section and same thermal resistance will have the lengths in the ratio

The two ends of a metal rod are maintained at temperatures $100 ^o C$ and $110^o C$. The rate of heat flow in the rod is found to be $4.0\ J/s$. If the ends are maintained at temperatures $200^o\  C$ and $210^o\ C$, the rate of heat flow will be…. $J/s$