Change in electrostatic potential energy of two spheres

[Pushoam]

We have two conducting spheres of radius r₁ and r₂ far away from each other. The first sphere has a charge Q. What is the change in electrostatic potential energy when they are connected together?
Before the connection ,
U_be = $\frac{Q^2}{8\pi\epsilon_0 r_1}$
After the connection ,
U_af = $\frac{Q^2}{8\pi\epsilon_0 r_1} \frac{r_1}{r_1+r_2}$
change in electrostatic potential energy =
U_af - U_be =
-$\frac{Q^2}{8\pi\epsilon_0 r_1} \frac{r_2}{r_1+r_2}$
I want to know that where does this energy get lost?
Does it get lost in the form of kinetic energy when the charges move around to redistribute themselves over the two conductors?
But , when again the charges become stationary, where do these K.E. go? Don't they get converted back into electrostatic energy?
Is there any way to know whether U_af >U_be or U_af <U_be before doing the calculation?

 

[Meir Achuz]

You have to include energy of each sphere, which is a rather complicated calculation.

 

[Pushoam]

You have to include energy of each sphere, which is a rather complicated calculation

I have included energy of each sphere.

 

[Nugatory]

Does it get lost in the form of kinetic energy when the charges move around to redistribute themselves over the two conductors?
But , when again the charges become stationary, where do these K.E. go?

It ends up as waste heat. Working out the details of how this happens may be fairly complicated, but when a closed system moves from a higher energy stable configuration to a lower energy stable configuration, the missing energy ends up as heat.