9.6 Entropy and the Second Law of Thermodynamics

Describing Entropy Changes in Systems

Entropy represents how energy is distributed within a system. It can be thought of as a measure of energy dispersion or the degree of disorder in a system.

• Entropy increases when energy spreads out more evenly throughout a system
• Entropy decreases when energy becomes more concentrated or organized
• Higher entropy generally means less energy is available to perform useful work

The second law of thermodynamics provides a fundamental rule about how entropy behaves in our universe. 🔒

• The total entropy of an isolated system can never decrease over time
• Entropy remains constant only during perfectly reversible processes (which are theoretical)
• In all real-world processes, the total entropy of an isolated system always increases
• This law explains why certain processes occur spontaneously in one direction but not the reverse

Energy Dispersion and Availability

Entropy can be understood as the tendency of energy to naturally spread out or disperse over time. 🌀

• When energy is highly concentrated in one area, the system has low entropy
• As energy disperses and spreads throughout the system, entropy increases
• This dispersion reduces the energy's ability to perform useful work
• Example: Heat always flows from hot objects to cold objects, never spontaneously from cold to hot

Entropy is a state function, which means it depends only on the current state of the system, not on how it reached that state.

• The entropy of a system depends on variables like temperature, pressure, and volume
• The path taken between states doesn't affect the total entropy change
• Maximum entropy occurs at thermodynamic equilibrium, when no further spontaneous changes occur

System Types and Entropy Behavior

How entropy behaves depends on whether a system is isolated, closed, or open:

• Isolated systems (no energy or matter transfer):
  • Entropy always increases until equilibrium is reached
  • Once at equilibrium, entropy remains constant
  • Example: A thermos containing hot coffee will eventually reach uniform temperature
• Closed systems (energy transfer but no matter transfer):
  • Entropy naturally increases over time as the system moves toward equilibrium
  • The system becomes more disordered as energy disperses
  • Example: A sealed container of hot water cooling down
• Open systems (both energy and matter transfer): 🚪
  • Entropy can decrease if energy or ordered matter enters the system
  • This doesn't violate the second law because the surroundings' entropy increases more
  • Example: Living organisms maintain internal order by increasing entropy in their surroundings

Practice Problem 1: Entropy Changes

Solution

a) The entropy of the hot block increases as its thermal energy spreads out. The entropy of the cold block also increases as it absorbs thermal energy and its molecules move more randomly.

b) The total entropy of the system increases. This is consistent with the second law of thermodynamics, which states that the entropy of an isolated system always increases during irreversible processes. Heat transfer between objects at different temperatures is an irreversible process.

c) The energy available to do work decreases. Initially, the temperature difference could have been used to perform work (like in a heat engine). As the blocks approach thermal equilibrium, this temperature difference diminishes, reducing the potential to do work. This illustrates how increasing entropy corresponds to decreasing ability to perform useful work.

Practice Problem 2: System Types and Entropy

Solution

a) This is an isolated system (assuming perfect insulation). Neither energy nor matter can enter or leave. According to the second law of thermodynamics, the entropy of this system cannot decrease. The ice and water will eventually reach thermal equilibrium at the melting point, with entropy increasing until equilibrium is reached.

b) This is an open system. Both energy (sunlight) and matter (CO₂, water, nutrients) can enter and leave. The entropy of this system can decrease locally as the plant creates ordered structures from simpler molecules. This doesn't violate the second law because the plant increases entropy elsewhere (through heat release to surroundings) by more than it decreases its own entropy.

c) This is an open system. Energy enters as electricity, and heat energy is expelled to the surroundings. The entropy of the food decreases as it cools (molecules move more slowly and orderly), but the refrigerator expels more entropy to its surroundings than it removes from the food. The total entropy of the universe still increases, satisfying the second law.