$A$ 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 ............. $\,kW$.

Three metal rods made of copper, brass, and steel, each with a cross-sectional area of $4 \,cm^2$, are joined as shown in the figure. Their lengths are $46 \,cm, 13 \,cm$, and $12 \,cm$ respectively. Their coefficients of thermal conductivity are $0.92, 0.26$, and $0.12$ respectively, all in $CGS$ units. The rods are thermally insulated from the surroundings except at the ends. The rate of flow of heat through the copper rod, in $cal \,s^{-1}$, is:

In the Ingen-Hauz's experiment,the wax melts up to lengths $10 \ cm$ and $25 \ cm$ on two identical rods of different materials. The ratio of thermal conductivities of the two materials is:

$A$ long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length $x$ of the bar from its hot end is best described by which of the following figures?

$A$ slab consists of two identical plates of copper and brass. The free face of the brass is at $0^{\circ} C$ and that of copper at $100^{\circ} C$. If the thermal conductivities of brass and copper are in the ratio $1: 4$,then the temperature of the interface is (in $^{\circ} C$)

An aluminium rod of length $1 \,m$ and a steel rod of length $2 \,m$, both having the same cross-sectional area, are soldered together end-to-end. The thermal conductivity of the aluminium rod and the steel rod is $200 \,Js^{-1} \,m^{-1} \,K^{-1}$ and $50 \,Js^{-1} \,m^{-1} \,K^{-1}$ respectively. The temperatures of the free ends are maintained at $300 \,K$ and $500 \,K$. What is the temperature of the junction (in $\,K$)?