Free Energy and Spontaneity in Open Systems

Open Systems and Laws of Thermodynamics

• When pressure and temperature are constant (open systems):
  • First Law: Change in thermal energy of system and universe are equal and opposite $( \Delta U<em>{system} = -\Delta U</em>{universe} )$, implying energy conservation $( \Delta U_{total} = 0 )$.
  • Second Law: Total change in entropy for system plus everything else must be $( \ge 0 )$ for real processes, or $( = 0 )$ for ideal reversible ones $( \Delta S<em>{total} = \Delta S</em>{system} + \Delta S_{universe} \ge 0 )$.
• The goal is to analyze the system without measuring the entire environment.

Free Energy

• Derived from combining the First and Second Laws under constant temperature conditions.
• Helmholtz Free Energy (F): $( \Delta F = \Delta U - T\Delta S )$
  • Useful for processes at constant volume and temperature.
• Gibbs Free Energy (G): $( \Delta G = \Delta H - T\Delta S )$
  • Most universally understood and easiest way to determine spontaneity at constant pressure and temperature (open systems).

Spontaneity and Gibbs Free Energy

• A process in an open system (constant P, T) will happen spontaneously if $( \Delta G < 0 )$.
• Influence of Temperature: For processes where ( \Delta H > 0 ) (endothermic) and ( \Delta S > 0 ) (entropy increases), a sufficiently high temperature can make the $( -T\Delta S )$ term large and negative, potentially outweighing $( \Delta H )$ and making ( \Delta G < 0 ), thus enabling spontaneity.
  • This explains why many processes become more active or occur at higher temperatures.