Entropy and Free Energy Flashcards

Chapter 10: Entropy and Free Energy

Recommended Textbook Problems

  • Energy, Enthalpy and Energy Changes Involving Ideal Gases and Physical Changes: 23, 27, 29
  • Entropy and the Second Law of Thermodynamics: 39, 41, 43, 45, 51
  • Free Energy and Chemical Reactions: 55, 57, 59, 65
  • Free Energy: Pressure Dependence and Equilibrium: 69, 71, 73, 77, 79, 87

Back to the Original Motivation

  • The original motivation was to convert a temperature gradient into usable work using a heat engine.
  • Heat Engine: A system that takes in heat, does work, and exhausts heat.
    • The diagram shows a system receiving heat and producing work (+w).
  • Efficiency is defined as the work output divided by the heat (energy) input: \text{Efficiency} = \frac{\text{work out}}{\text{heat (Energy) in}}
  • The goal was to improve efficiency, which was a major focus in the late 1800s and early 1900s.
  • Early heat engines were only 1-3% efficient, representing a significant loss of energy (lost ).
  • Work is obtained from the system expanding.
  • Two ways to improve efficiency:
    • Get more work out.
    • Require less energy to compress the system/surroundings.

Work Changes with Path (10-2)

  • Work is path-dependent.
  • The example illustrates splitting a process into two steps.
  • Less work is required when the process is split into multiple steps.
  • The diagram shows a piston with sand on top being lowered in multiple stages.
    • Initial state: Sand with mass m.
    • Two-step process: Sand is removed in two steps of 0.5m each.
    • Final state: Piston lowered.
  • Less work is required with more steps.
  • In the ideal scenario, work is carried out by removing one grain of sand at a time, implying an infinite number of steps.
  • Infinite number of steps equates to an infinite amount of time.

Reversible Processes vs Cyclic Processes

  • Reversible Process:
    • The most work you can get out of the system.
    • The least work required to compress the system.
    • Cannot tell which direction we are heading.
    • The universe returns to its original state (ideal).
    • Not possible in reality.
  • Cyclic Process:
    • The system returns to its original position.
    • State functions (e.g., \Delta E) are the same, but work is different.
  • All real processes change the surroundings in a permanent way.
    • Heat
    • Entropy

Entropy: The Macroscopic View 10.3

  • In the 1850s, a new state function, Entropy (S), was defined to simplify the math relating Q, w, T, \Delta H, \Delta E, etc.
  • \Delta S = \frac{q{rev}}{T} where q{rev} is how much thermal energy is transferred.
  • It was soon realized that entropy tells us something about the "disorder" of the universe.
  • Entropy increases (\Delta S > 0$$):
    • Heat flows from hot to cold.
    • Particles spread out as much as possible.
      • Gas particles fill their container.