Batteries in Series: Understanding Voltage Addition

[Slava]

Hey Guys, there is one question which is bugging me for the last couple of weeks. I am an embedded software engineer and when it comes to very deep understanding what is going it in the electrical circuits I struggle a lot. Recently I have decided to go through the course of physics again especially electrostatics and electrodynamics and being an engineer started asking questions to myself which never thought about when I was a student.
One of the questions which I bumped into and can't find an answer is this one:

Suppose I have two batteries connected in series. Why the voltages are added together.
I understand roughly physics and electro-chemistry of how the battery works alone. But I am getting lost when
two batteries are connected series. How do electrons get more potential energy?

 

[Simon Bridge]

Welcome to PF;
Same reason that if you put a hill on top of another hill the heights are added together.
The electrons get more energy the same way that carrying a weight up both hills gets it more energy.
Starting from the highest +ve side - the first battery lifts the electrons through V1 and delivers them to the +ve side of the next battery which lifts them a further V2 for a total of V1+V2.

(Conventional charges go the other way...)