First Law of Thermodynamics

The first law of thermodynamics is the energy-balance rule for a system: any increase in a system’s internal energy must come from heat entering the system, from work being done on it, or both. The sign convention in
U = Q - W means Q is positive when heat flows in, and W is positive when the system does work on its surroundings, so that work output reduces the system’s internal energy. It is essentially conservation of energy applied to thermal processes.

Use this formula whenever you need to track how heating, compression, expansion, or engine-like processes change a gas or thermodynamic system. It is common in problems about pistons, refrigerators, boilers, and any closed system where heat transfer and work are both involved.

• Using the wrong sign for work, especially confusing work done by the system with work done on the system
• Forgetting that Q is positive only when heat enters the system
• Assuming internal energy change depends only on temperature and ignoring work or heat transfer