What is first law of thermodynamics?
It is a law that relates the exchange of energy of a system with its internal energy.
If you have a system (say, a gas) it is possible to change its internal energy by exchanging heat or work with the surrounding.
The first law tells us that when heat and/or work is exchanged the internal energy of the system changes.
This is written in mathematical form as:
The signs are a bit tricky though; I studied this law as I wrote it because there is a convention in it:
When heat enters the System it is considered POSITIVE;
When heat exits the System it is considered NEGATIVE;
When work enters the System it is considered NEGATIVE;
When work exits the System it is considered POSITIVE;
[I suspect that this convention comes from the Industrial Revolution and the birth of Thermodynamics; a machine that gave out work meant GOOD work...that gave money; while a machine that required work to operate meant BAD work or money you had to input. Heat out was also bad because meant loss in performance and so in money gained....I think]
The first law may seem complicated at first but you have to think at it in terms of exchange of energy.
I give you an example:
Imagine you have a gas in a cylinder that has a movable piston; visualize the internal energy of the gas as the vibration and movement of the gas particles.
Now let us give energy to the gas:
1) we heat the gas (we lit a fire under the cylinder): energy is communicated to the gas through heat
ex: you give
2) we compress the gas: work is done on the gas
ex: you give
3) Now you heat the cylinder and let the piston expand: the internal energy increases because the heat BUT also decreases because work is done by the system!!!
ex: heat in (positive)
What I do it is always let the minus (in red below) of the formula fixed and insert in brackets the numerical values for
Hope it helps!