The First Law: Conservation of Energy and Internal Energy

The first law of thermodynamics is a conservation law: energy is neither created nor destroyed, it is transformed and transferred. For a closed system, it is written Delta U = Q + W, where Delta U is the change in internal energy, Q the heat exchanged and W the work exchanged, with the receiver convention: Q and W are counted as positive when the system receives them, negative when it gives them up.

Internal energy U gathers the microscopic kinetic energy of the particles (their agitation) and their interaction potential energy. It is a state function: its change between an initial state and a final state depends only on these two states, never on the path taken to go from one to the other. This is very different from Q and W, which do depend on the path followed during the transformation.

Take a concrete example: a gas enclosed in a cylinder receives heat from a flame (Q positive) and pushes back a piston, so it supplies work to the outside (W negative in the receiver convention). If Q = 300 J and the gas supplies 120 J, then W = -120 J and Delta U = 300 - 120 = 180 J: the internal energy of the gas increases by 180 joules.

Common pitfall: do not confuse "the system receives work" with "the system supplies work". The sign of W depends solely on the chosen convention, but once chosen, you must stick to it throughout the calculation. Another pitfall: for an isolated system, no exchange takes place with the outside, so Q = 0 and W = 0, and Delta U = 0: its internal energy remains strictly constant.

The diagram below represents this balance: the system is delimited by an imaginary boundary through which heat and work pass, changing its internal energy.

             (system boundary)
         ........................
         :                      :
   Q --> :       (system)       :
         :      U (internal     :
         :      energy)         :
         :                      :
         ........................
                   ^
                   |
                   W

   Delta U = Q + W    (receiver convention: positive if received)