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?

One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of lengths $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two sections is

One end of a copper rod of length $1.0\;m$ and area of cross-section ${10^{ - 3}}$ is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is $92\;cal/m{\rm{ - }}s{{\rm{ - }}^o}C$ and the latent heat of ice is $8 \times {10^4}cal/kg$, then the amount of ice which will melt in one minute is

Three rods of Copper, Brass and Steel are welded together to form a $Y$ shaped structure. Area of cross - section of each rod $= 4\ cm^2$ . End of copper rod is maintained at $100^o C $ where as ends ofbrass and steel are kept at $0^o C$. Lengths of the copper, brass and steel rods are $46, 13$ and $12\ cms$ respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are $0.92, 0.26$ and $0.12\ CGS$ units respectively. Rate ofheat flow through copper rod is ....... $cal\, s^{-1}$

Give definition, unit and dimensional formula of thermal conductivity.

There are two identical vessels filled with equal amounts of ice. The vessels are of different metals., If the ice melts in the two vessels in $20$ and $35$ minutes respectively, the ratio of the coefficients of thermal conductivity of the two metals is