The lengths of two rods made of the same metal and having the same area of cross-section are $0.6 \ m$ and $0.8 \ m$ respectively. The temperatures at the ends of the first rod are $90^{\circ}C$ and $60^{\circ}C$,and those for the second rod are $150^{\circ}C$ and $110^{\circ}C$. For which rod will the rate of heat conduction be greater?

The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_1$ and $T_2$ $(T_1 > T_2)$. The rate of heat transfer,$\frac{dQ}{dt}$,through the rod in a steady state is given by:

$A$ conducting rod of length $1 \,m$ has an area of cross-section $10^{-3} \,m^2$. One end is immersed in boiling water $(100^{\circ} C)$ and the other end in ice $(0^{\circ} C)$. If the coefficient of thermal conductivity of the rod is $96 \,cal/(s \cdot m \cdot ^{\circ}C)$ and the latent heat of fusion for ice is $8 \times 10^4 \,cal/kg$,then the amount of ice that will melt in one minute is:

Which of the following cylindrical rods will conduct the most heat when their ends are maintained at the same steady temperature difference?

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity $K_{1}, K_{2},$ and $K_{3}$,respectively. They are joined together at their ends to make a long rod. One end of the long rod is maintained at $100^{\circ} C$ and the other at $0^{\circ} C$. If the joints of the rod are at $70^{\circ} C$ and $20^{\circ} C$ in steady state and there is no loss of energy from the surface of the rod,the correct relationship between $K_{1}, K_{2}$ and $K_{3}$ is:

The thermal conductivity of copper is $9$ times that of steel. Find the temperature of the junction of copper and steel in the composite rod as shown in the figure (in $^oC$).