The first law of thermodynamics is an energy conservation statement

The equation and its terms

• The first law is fundamentally a restatement of the conservation of energy applied to thermodynamic systems.
• In the AQA sign convention:
  • $\Delta U$ = increase in internal energy (J)
  • $Q$ = energy supplied to the system by heating (J)
  • $W$ = work done by the system (J)
• Crucially, the sign convention matters:
  • $Q$ is positive if heat energy is added to the system, negative if removed
  • $\Delta U$ is positive if the internal energy increases, negative if it decreases
  • $W$ is positive if work is done by the gas (gas expands), negative if work is done on the gas (gas is compressed)

Open and closed systems

• A systemA region of space containing a quantity of gas, defined by its boundary. The first law applies to any system, not just gases. is a region of space containing a quantity of gas.
• An open system allows gas or vapour to flow into and out of the region. Examples include gas expanding through a nozzle or steam passing through a turbine.
• A closed system keeps the gas or vapour within the boundary, although the boundary can expand or contract. Examples include gas expanding in a cylinder by moving a piston.
• In both types, work can cross the boundary.
• The first law applies to all situations, not just gases.

Work done by a gas at constant pressure

• When the volume of a gas changes at constant pressure, the work done is:

• Where $p$ is the pressure (Pa) and $\Delta V$ is the change in volume (m$^3$).
• This equation assumes the surrounding pressure does not change as the gas expands, which is true when expanding against atmospheric pressure.