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

The intensity of radiation emitted by the Sun has its maximum value at a wavelength of $510\,\, nm$ and that emitted by the North Star has the maximum value at $350\,\, nm$. If these stars behave like black bodies then the ratio of the surface temperature of the Sun and the North Star is

A cylinder of radius $R$ made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity $K_2.$ The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

Hot water cools from $60\,^oC$ to $50\,^oC$ in the first $10\, min$ and to $42\,^oC$ in the next $10\, min$. The temperature of the surrounding is  …….. $^oC$

A body cools from $62\,^oC$ to $50\,^oC$ in $10\, minutes$ and to $42\,^oC$ is next $10\, minutes$. The temp. of surrounding is …….. $^oC$