Two liquid A & B having densities `2rho` and `rho` respectively, are kept in a cylindrical container separated by a partition as shown in figure. The height of each liquid in the container is h and area of cross section of the container is A. Now the partition is removed. Calculate change in gravitational potential energy (`DeltaU`) of the system (a) assuming that the two liquids mix uniformly. (b) Assuming that the two liquids are immiscible. What do you conclude from the sign of `DeltaU` in the above two cases?

Answer

`(a) 1/2 rhoAh^(2) g`
(b) `-rhoAh^(2)g`
The positive sign of `DeltaU` means external work will be required to mix the two liquids uniformly. `DeltaU` is negative in second case which means the heavier liquid will automatically move to lower side.