Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2\,T$ and $3\,T$ respectively. The temperature of the middle (i.e. second) plate under steady state condition is

A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature $120\ ^oC$ , then

Assuming the sun to be a spherical body of radius $R$ at a temperature of $TK$ , evaluate the total radiant power, incident on the earth, at a distance $r$ from the sun, is (Where $r_0$ is the radius of the earth and $\sigma $ is Stefan s constant.)

Two rods $A$ and $B$ of different materials but same cross section are joined as in figure. The free end of $A$ is maintained at $100^o C$ and the free end of $B$ is maintained at $0^o C$. If $l_2 = 2l_1, K_1 = 2K_2$ and rods are thermally insulated from sides to prevent heat losses then the temperature $\theta$ of the junction of the two rods is …….. $^oC$

Two stars emit maximum radiation of wavelength $3600\,\mathop A\limits^o $  and $4800\,\mathop A\limits^o $  respectively. The ratio of their temperatures is