How can the first law of thermodynamics be mathematically expressed?

The first law of thermodynamics is a fundamental principle that relates the heat energy added to a system, the work done on or by the system, and the change in the internal energy of that system. Mathematically, this law is commonly expressed as the change in internal energy of a system (ΔE) being equal to the heat added to the system (Q) minus the work done by the system (W).

This relationship can be written as:

ΔE = Q - W

This means that when heat is added to a system, it can increase the internal energy, but if the system does work on its surroundings, the internal energy will decrease by the amount of work done. This formulation correctly captures the conservation of energy, showing how energy can be transferred in a system through heat and work, while still accounting for the internal energy changes.

In contrast, other mathematical expressions provided do not accurately represent the principles behind the first law of thermodynamics and do not reflect the proper positive and negative relationships between heat, work, and internal energy.