AP Physics 2- 9.6 Entropy and the Second Law of Thermodynamics- Study Notes- New Syllabus

Entropy:

Entropy measures the tendency of energy to spread out or the unavailability of energy to do work.

• Localized energy will naturally disperse over time.
• Entropy is a state function: it depends only on the current state or configuration of the system, not on the path taken.
• Maximum entropy occurs when a system reaches thermodynamic equilibrium.
• The change in a system’s entropy depends on interactions with its surroundings.

Mathematical Expression:

\( \Delta S = \displaystyle \int \dfrac{dQ_{rev}}{T} \)

• \( \Delta S \): Change in entropy
• \( dQ_{rev} \): Infinitesimal heat absorbed reversibly
• \( T \): Absolute temperature at which heat is transferred

Essential conclusions:

• Entropy is a measure of energy dispersal and disorder.
• Isolated systems always move toward maximum entropy (thermodynamic equilibrium).
• Reversible processes maintain total entropy, irreversible processes increase it.
• Entropy changes in a system are influenced by energy exchanges with surroundings.

Second Law of Thermodynamics:

The total entropy of an isolated system can never decrease. It remains constant only when all processes are reversible.

• Isolated systems spontaneously evolve toward thermodynamic equilibrium, the state of maximum entropy.
• In a closed system, entropy can decrease because energy can be exchanged with the surroundings.