The ratio of thermal conductivity of two rods of different materials is $5 : 4$. The two rods of same area and same thermal resistance will have lengths is the ratio

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$, while box $B$ contains one mole of helium at temperature $(7/3)$ $T_0$. The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (Ignore the heat capacity of boxes). Then, the final temperature of gases, $T_f$, in terms of $T_0$ is

A piece of iron is heated in a flame. It first becomes dull red then becomes reddish yellow and finally turns to white hot. The correct explanation for the above observation is possible by using

A wall has two layers $A$ and $B,$ each made of different material. Both the layers have the same thickness. The thermal conductivity for $A$ is twice that of $B$ and under steady condition, the temperature difference across the wall is $36\,^oC.$ The temperature difference across the layer $A$ is....... $^oC$

If the wavelengths of maximum intensity of radiations emitted by the sun and the moon are $0.5\times10^{-6}\, m$ and $10^{-4}\, m$ respectively. The ratio of their temperature is

Two rods are connected as shown. The rods are of same length and same cross sectional area. In steady state, the  temperature $\left( \theta  \right)$ of the interface will be........ $^oC$