The Missing Energy

[cupid.callin]

I was studying capacitors when I came across these three questions:
Please refer the jpg with the topic.

Note: I wrote the quoted text before I realized I could post the pic of questions … but I had written all this anyway and didn’t wanted it to go to waste … so I posed it anyway!!!!

1st: A parallel plate capacitor is connected with a battery and after it is fully charged the separation b/w the plates is increased, --- of course capacitance decrease and charge flows backwards --- I am supposed to find heat generated in the process …

2nd: A capacitor is charged to some voltage V and then disconnected from it and connected to another battery of voltage V’ (<V) … so this time the current flows backwards … question is again to calculate the heat.

3rd: this time a capacitor is connected to a battery, removed after long time, connected to a capacitor of smaller capacitance!!! And again I need to calculate the heat generated!!!

Answer to 1st=
1st= 0
2st= 7.2 mJ
3st= 1.77 mJ

Now…
How am I supposed to know how to find the heat generated??? What basis do I use… well my questions are insane I know... but just because I have no idea what to do!!
Please help me find a way to find heat generated … not only for these cases but also for any other random case!!!

 

[collinsmark]

To start, note that the energy stored in a capacitor (of a given, constant capacitance C and voltage V) is

E = ½CV².​

You'll have to use this equation a little differently for each part of the problem. But essentially, it means finding the equivalent capacitance before and after; and also finding the voltage across the equivalent terminals, before and after. Then compare the energies before and after.

 

[cupid.callin]

But for Ques 3 work done on battery will be QV'
Shouldn't that be heat produced???

 

[cupid.callin]

Well I'll try what u said and get back if it works!!!!

Thanks for help