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

When a system is taken from state $$i$$ to state $$f$$ along the path iaf, it is found that $$Q=50$$ cal and $$W=20$$ $$cal$$. Along the path $$ibf$$ $$Q=36$$ $$cal.$$ $$W$$ along the path $$ibf$$ is

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 contains one mole of helium at temperature $$\left( {{7 \over 3}} \right){T_0}.$$ 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 the gases, $${T_f}$$ in terms of $${T_0}$$ is

Assuming the Sun to be a spherical body of radius $$R$$ at a temperature of $$TK$$, evaluate the total radiant powered incident of Earth at a distance $$r$$ from the Sun

Where r₀ is the radius of the Earth and $$\sigma $$ is Stefan's constant.