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

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

A cylinder of radius $R$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$. The thermal conductivity of the material of the inner cylinder is $K_1$ and that of the outer cylinder is $K_2$. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is

Which of the following statements is/are $CORRECT$ Correct option are

$(i)$ a body with large reflectivity is a poor emitter

$(ii)$ a brass tumbler feels much colder than a wooden tray on a chilly day

$(iii)$ the earth without its atmosphere would be inhospitably cold

$(iv)$ heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water

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 length $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two section is