First law of thermodynamics

The first law of thermodynamics states that the change in energy of a closed system equals the sum of heat transferred to it and work done to it

This is basically a statement of conservation of energy.

Here $\db$ denotes an inexact differential. This means that there are no functions $Q$ and $W$ of which $\db Q$ and $\db W$ are differentials. There is no measurement of a system I could perform which would tell me it’s “heat” or it’s “work”. $\d U$ is an exact differential, so I could on the other hand measure the energy or temperature.

In other words, $U$ is a state function, while $Q$ and $W$ are not.