$A$ cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat $Q$ in time $t$. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod,when placed in thermal contact with the two reservoirs in time $t$?

Three rods of the same dimensions have thermal conductivities $3k, 2k$ and $k$. They are arranged as shown,with their ends at $100\,^{\circ}C, 50\,^{\circ}C$ and $0\,^{\circ}C$. The temperature of their junction is

Consider two rods of same length and different specific heats $(S_{1}, S_{2})$,conductivities $(K_{1}, K_{2})$ and area of cross-sections $(A_{1}, A_{2})$ and both having temperatures $T_{1}$ and $T_{2}$ at their ends. If the rate of loss of heat due to conduction is equal,then:

The area of the glass of a window of a room is $10\;m^2$ and thickness is $2\;mm$. The outer and inner temperatures are $40^{\circ}C$ and $20^{\circ}C$ respectively. The thermal conductivity of glass in the $MKS$ system is $0.2\;W/(m\cdot K)$. The heat flowing into the room per second will be:

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

$A$ copper pipe of length $10 \,m$ carries steam at temperature $110^{\circ} C$. The outer surface of the pipe is maintained at a temperature $10^{\circ} C$. The inner and outer radii of the pipe are $2 \,cm$ and $4 \,cm$,respectively. The thermal conductivity of copper is $0.38 \,kW / m /^{\circ} C$. In the steady state,the rate at which heat flows radially outward through the pipe is closest to ............. $\,kW$.