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.