Energy, Entropy, and Free Energy Notes

Energy, Entropy, & Free Energy

Introduction

• To understand life, we need to grasp the concepts of energy, entropy, and free energy and their relationships. We'll start with an easily understandable example and then apply it to chemistry.

Conservation of Energy

• Energy is conserved.
• The statement that "energy is the ability to do work" has a flaw.

Rock on a Cliff Example

• Consider a rock on top of a cliff.
• Before falling, its energy is potential energy.
• After falling, its energy is dispersed as heat.
• Energy remains constant, but does the ability to do work stay constant?

Work Example

• To drive a stake into the ground, work needs to be done.
• Two approaches:
  1. Dropping a rock on the stake.
  2. Dropping a rock onto the ground next to the stake and using the dispersed heat.
• If energy is the ability to do work, both approaches should be equal, but they are not.

Dispersed Heat

• It's difficult to harness energy in the form of dispersed heat.
• It's not very efficient for doing work, but it is still energy.

Entropy

• Energy is critical, but insufficient on its own.
• Entropy is a key missing element.
• Entropy: A measure of the amount of energy that has been dispersed and is not readily available to do work.
• The energy is not destroyed or reduced but dispersed.

Energy and Entropy Over Time

• Energy stays constant.
• Entropy increases with time.
• Energy disperses and spreads out, becoming less useful for doing work.
• The amount of energy available to do work declines with time.

Rock Falling off a Cliff (Video Reference)

• The rock is pushed off the edge of the cliff and lands on the ground.
• Energy is conserved; it is the same before and after the rock falls.
• Entropy increases; the initial potential energy converts to heat, which disperses and becomes less able to do work.

Post-Fall Analysis

• After the rock comes to rest, consider whether the energy (now as heat) could launch the rock back to the top of the cliff.
• Although total energy is conserved, much of it has become unavailable to do work. Entropy has increased.
• There is no longer enough useful energy to do the work of lifting the rock back to the top of the cliff.
• It would be impractical to use the dispersed heat to lift the rock.

A Note on "Useless Energy"

• Dispersed heat energy is referred to as useless.
• Heat itself has uses; for example, it is useful if you're cold.
• Efficient heat engines can concentrate heat in a boiler before it disperses.
• After heat becomes dispersed, it is, for all practical purposes, useless.
• The terms "dispersed heat," "heat," and "useless energy" are used interchangeably, as they're mostly true.

State of the Universe

• Within the universe, there is:
  • A constant amount of energy
  • A constantly increasing amount of useless energy
  • A constantly decreasing amount of useful energy

Free Energy

• Free energy is the amount of energy available to do work.
• $Free\ Energy = Total\ Energy - Useless\ Energy$
• The total amount of energy is conserved; energy cannot be created or destroyed. However, the amount of useless energy always increases. Therefore, the amount of free energy always decreases.

Free Energy Example

• Start with:
  • 100 units of total energy
  • 10 units of useless energy
  • 90 units of free energy
• At a later time, the amount of useless energy increases to 20 units.
• Free Energy Calculation:
  • $Free\ Energy = Total\ Energy - Useless\ Energy$
  • $Free\ Energy = 100 - 20$
  • $Free\ Energy = 80$
• At a later time:
  • 100 units of total energy
  • 20 units of useless energy
  • 80 units of free energy