If two soap bubbles of different radii are connected by a tube

If the temperature of the sun were to increase from $$T$$ to $$2T$$ and its radius from $$R$$ to $$2R$$, then the ratio of the radiant energy received on earth to what it was previously will be

One mole of ideal monatomic gas $$\left( {\gamma = 5/3} \right)$$ is mixed with one mole of diatomic gas $$\left( {\gamma = 7/5} \right)$$. What is $$\gamma $$ for the mixture? $$\gamma $$ Denotes the ratio of specific heat at constant pressure, to that at constant volume

Two thermally insulated vessels $$1$$ and $$2$$ are filled with air at temperatures $$\left( {{T_1},{T_2}} \right),$$ volume $$\left( {{V_1},{V_2}} \right)$$ and pressure $$\left( {{P_1},{P_2}} \right)$$ respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be