Equation #7: First law of thermodynamics
The first law of thermodynamics is essentially the restatement of the law of conservation of Energy. In thermodynamics, we write this conservation law a little differently. We say that the internal energy of a system (U) can be changed only by either heating it up (or cooling it down), or by doing work on (or extracting work from) it.
The act of heating increases U(hence we write +Q) while extracting work(e.g. in generating electricity using water on turbines) decreases it(hence we write -W).
It is simple yet very powerful law which took a long time to be accepted, mainly because the concept of heat was not understood properly (Heat is the energy in transfer by virtue of temperature difference).
For an interesting take on the history of the law and the concept of heat, seehttps://www.youtube.com/watch?v=6IHg5fJZN6s
Some experiments(they take extracted work with the +sign and work done on the system with -sign):
For more equations like this, see Famous Equations in Physics