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

If two metallic plates of equal thicknesses and thermal conductivities $K_1$ and $K_2$ are put together face to face and a common plate is constructed,then the equivalent thermal conductivity of this plate will be

$A$ thermocol box has a total wall area (including the lid) of $1.0 \,m^2$ and wall thickness of $3 \,cm$. It is filled with ice at $0^{\circ} C$. If the average temperature outside the box is $30^{\circ} C$ throughout the day, the amount of ice that melts in one day is (Given: $K_{\text{thermocol}} = 0.03 \,W/mK$, $L_{\text{fusion(ice)}} = 3.00 \times 10^5 \,J/kg$) (in $\,kg$)

On heating one end of a rod,the temperature of the whole rod will be uniform when

$A$ solid cylinder of radius $R$ made of a material of thermal conductivity $K_{1}$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of a material of thermal conductivity $K_{2}$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

$A$ brass boiler has a base area of $0.15\; m^{2}$ and thickness $1.0\; cm$. It boils water at the rate of $6.0\; kg/min$ when placed on a gas stove. Estimate the temperature (in $^oC$) of the part of the flame in contact with the boiler. Thermal conductivity of brass $= 109\; J s^{-1} m^{-1} K^{-1}$; Heat of vaporisation of water $= 2256 \times 10^{3}\; J kg^{-1}$.