How does the first law of thermodynamics describe heat and work?

The first law of thermodynamics, which is a statement of the law of conservation of energy, establishes a strict energy accounting system for a system interacting with its surroundings. It describes the relationship between heat ($Q$), work ($W$), and the change in internal energy ($\Delta U$) using the equation:12

$$\Delta U=Q-W$$

In this framework, the change in a system's internal energy is equal to the heat added to the system from its surroundings minus the work done by the system on its surroundings.23

A critical distinction exists between these quantities:
* Internal Energy ($U$): This is a state function, meaning its value depends only on the current state of the system, not the path taken to reach it.14
* Heat and Work ($Q$ and $W$): These are not state functions; they are path-dependent quantities. Their values depend on the specific process used to transition between states, much like how a bank account balance (the state) can be reached through various combinations of deposits and withdrawals (the process).14