The two opposite faces of a cubical piece of iron (thermal conductivity $= 0.2\, CGS$ units) are at ${100^o}C$ and ${0^o}C$ in ice. If the area of a surface is $4c{m^2}$, then the mass of ice melted in $10$ minutes will be ...... $gm$
$30 $
$300 $
$5$
$50$
What is the temperature (in $^oC$) of the steel-copper junction in the steady state of the system shown in Figure Length of the steel rod $=15.0\; cm ,$ length of the copper rod $=10.0\; cm ,$ temperature of the furnace $=300^{\circ} C ,$ temperature of the other end $=0^{\circ} C .$ The area of cross section of the steel rod is twice that of the copper rod. (Thermal conductivity of steel $=50.2 \;J s ^{-1} m ^{-1} K ^{-1} ;$ and of copper $\left.=385 \;J s ^{-1} m ^{-1} K ^{-1}\right)$
The ends of two rods of different materials with their thermal conductivities, radii of cross-sections and lengths all are in the ratio $1:2$ are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is $4\;cal/\sec $, that in the shorter rod in $cal/\sec $ will be
Two thin metallic spherical shells of radii ${r}_{1}$ and ${r}_{2}$ $\left({r}_{1}<{r}_{2}\right)$ are placed with their centres coinciding. A material of thermal conductivity ${K}$ is filled in the space between the shells. The inner shell is maintained at temperature $\theta_{1}$ and the outer shell at temperature $\theta_{2}\left(\theta_{1}<\theta_{2}\right)$. The rate at which heat flows radially through the material is :-
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 identical square rods of metal are welded end to end as shown in figure $(a)$. Assume that $10\, cal$ of heat flows through the rods in $2\, min$. Now the rods are welded as shown in figure, $(b)$. The time it would take for $10$ cal to flow through the rods now, is ........ $\min$