A system goes from $$A$$ to $$B$$ via two processes $$I$$ and $$II$$ as shown in figure. If $$\Delta {U_1}$$ and $$\Delta {U_2}$$ are the changes in internal energies in the processes $$I$$ and $$II$$ respectively, then

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

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

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $$K$$ and $$2K$$ and thickness $$x$$ and $$4x,$$ respectively, are $${T_2}$$ and $${T_1}\left( {{T_2} > {T_1}} \right).$$ The rate of heat transfer through the slab, in a steady state is $$\left( {{{A\left( {{T_2} - {T_1}} \right)K} \over x}} \right)f,$$ with $$f$$ equal to