AP Physics 2: Thermodynamic Cycles, Probability, and Entropy

First Law of Thermodynamics

States that the change in internal energy of a system is equal to the heat added to the system plus the work done on the system.

$U$

Change in Internal Energy; the energy stored in the motion of the gas particles, directly proportional to Temperature.

Heat ($Q$)

Energy transferred due to temperature difference, positive if added to the system and negative if removed.

Work ($W$)

Energy transferred by mechanical force, positive for work done on the gas (compression) and negative for work done by the gas (expansion).

Isobaric Process

A process at constant pressure where the gas expands or contracts.

Isochoric / Isovolumetric Process

A process at constant volume where the gas does no work due to no area under a vertical line.

Isothermal Process

A process at constant temperature that involves heat exchange to maintain temperature during expansion/compression.

Adiabatic Process

A process with no heat transfer, where changes occur rapidly or the system is insulated.

Entropy ($S$)

A measure of disorder or randomness of a system, reflecting the number of ways a system can be arranged.

Microstate vs. Macrostate

Microstate: specific position and velocity of particles; Macrostate: overall description of the system.

$S = rac{Q}{T}$

Formula for change in entropy when heat is transferred at constant temperature.

Thermodynamic Cycle

A series of processes that returns the gas to its initial state, with net work equal to the net heat exchanged.

Clockwise Cycle

A thermodynamic cycle representing a heat engine where net work is done by the gas.

Counter-Clockwise Cycle

A thermodynamic cycle representing a refrigerator or heat pump where net work is done on the gas.

Geometric area on PV diagram

Represents the work done during a thermodynamic process.

Isotherm

The curve on a PV diagram representing a process at constant temperature.

Expansion (Moving Right)

A process where gas performs work, resulting in negative work done on the system.

Compression (Moving Left)

A process where work is done on the gas, resulting in positive work.

Conservation of Energy

The principle that energy cannot be created or destroyed, only transformed, as stated in the First Law of Thermodynamics.

Total Entropy

In any isolated system, total entropy never decreases, always increasing or remaining constant.

Heat Flow Direction

Heat naturally flows from hot to cold, reflecting the Second Law of Thermodynamics.

Probability and Entropy

The relationship where systems with more possible microstates are more probable and have higher entropy.

Work during Isobaric Process

W = -P∆V; work done is calculated based on pressure and change in volume.

Work during Isochoric Process

W = 0; no work is done since volume remains constant.

Work during Isothermal Process

All work done must be compensated by heat transfer to keep temperature constant.

Work during Adiabatic Process

ΔU = W, as no heat transfer occurs, work directly changes internal energy.

Common Mistakes in Thermodynamics

Includes confusing signs of work, misinterpreting adiabatic processes, and misunderstanding path dependence.