9.6 Entropy and the Second Law of Thermodynamics

What Entropy Means in AP Physics 2

In AP Physics 2, entropy is treated qualitatively. Entropy describes the tendency of energy to spread out and the fact that some of a system's energy becomes unavailable to do useful work. The second law of thermodynamics says the total entropy of an isolated system can never decrease.

This is why spontaneous processes have a direction: localized energy tends to disperse, and isolated systems move toward thermodynamic equilibrium. A closed system's entropy can decrease if energy leaves the system, but the total entropy of the system plus surroundings still follows the second-law idea.

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Describing Entropy Changes in Systems

Entropy represents how energy is distributed within a system. In AP Physics 2, entropy is best described qualitatively as the tendency of energy to spread out and as a measure of how much of a system's energy is unavailable to do useful work.

• 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

How Interactions with Surroundings Determine Entropy Change

A system's entropy change depends on how the system interacts with its surroundings. If energy is transferred into or out of the system, the system's entropy can change. This is why isolated systems must have nondecreasing total entropy, while closed systems can sometimes have decreasing entropy if energy leaves the system.

System Types and Entropy Behavior

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

• Isolated systems (no energy or matter transfer):
  • Entropy always increases until equilibrium is reached
  • Once at equilibrium, entropy remains constant
  • Isolated systems spontaneously move toward thermodynamic equilibrium
  • Example: A thermos containing hot coffee will eventually reach uniform temperature
• Closed systems (energy transfer but no matter transfer):
  • The entropy of a closed system can either increase or decrease because energy can be transferred into or out of the system
  • Unlike an isolated system, a closed system is not required to have nondecreasing entropy at every moment
  • A closed system often moves toward equilibrium, but if energy leaves the system, its entropy can decrease
  • Example: A sealed container of hot water cooling down can have decreasing entropy as thermal energy leaves the container

AP Physics 2 primarily focuses on isolated and closed systems for entropy discussions. Some real systems exchange both energy and matter with their surroundings, but detailed treatment of open systems is beyond the scope required here.

Practice Problem 1: Entropy Changes

Solution

a) The entropy of the hot block decreases because it loses thermal energy to the colder block. The entropy of the cold block increases because it gains thermal energy. The increase in entropy of the cold block is greater than the decrease in entropy of the hot block, so the total entropy of the isolated system increases.

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: Isolated vs. Closed Systems

Solution

a) This is an isolated system (assuming perfect insulation). No energy or matter enters or leaves, so its total entropy cannot decrease. It will move toward thermodynamic equilibrium.

b) This is a closed system. Matter does not leave the can, but thermal energy can leave to the surroundings. Because energy leaves the system, the entropy of the soup can decrease.

c) This is an isolated system if the container is perfectly insulated and sealed. The system will spontaneously move toward thermodynamic equilibrium, and its total entropy will not decrease.