Mastering Thermodynamics: Energy Conservation, Entropy, and Cycles

First Law of Thermodynamics

The law of Conservation of Energy applied to a thermal system, stating that energy cannot be created or destroyed, only transferred or transformed.

$ riangle U$ (Internal Energy)

The change in the total kinetic and potential energy of the gas molecules, which depends only on Temperature (T) for an ideal gas.

$Q$ (Heat)

Energy transferred due to a temperature difference; positive when heat is added to the system, negative when heat is lost.

$W$ (Work)

Energy transferred by mechanical means; positive when work is done on the system, negative when work is done by the system.

Isobaric Process

A thermodynamic process where pressure remains constant; represented as a horizontal line on a PV graph.

Isochoric Process

A thermodynamic process where volume remains constant; represented as a vertical line on a PV graph.

Isothermal Process

A thermodynamic process where temperature remains constant; represented as a curved line (Hyperbola) on a PV graph.

Adiabatic Process

A thermodynamic process with no heat transfer; represented as a steep curve on a PV graph.

Heat Engine

A device that converts thermal energy into mechanical work, operating in a cycle.

Thermal Efficiency ($e$)

A measure of how much of the input heat equals useful work, expressed as a ratio.

Carnot Efficiency

The theoretical maximum efficiency for any heat engine, depending only on the temperatures of the reservoirs.

Entropy ($S$)

A quantitative measure of disorder or randomness in a system, increasing with the number of accessible microstates.

Entropy Statement (Second Law)

The total entropy of the universe always increases for irreversible natural processes and remains constant for reversible processes.

Heat Flow Statement (Second Law)

Heat never flows spontaneously from a cold object to a hot object.

Efficiency Statement (Carnot)

No heat engine operating between two given heat reservoirs can be more efficient than a Carnot engine.

Sign Convention for Work

Work done on the system is positive (compression); work done by the system is negative (expansion).

Absolute Value of Work ($|W|$)

Equal to the area under the curve in a Pressure-Volume (PV) diagram.

$ riangle S = rac{Q}{T}$

Formula for determining entropy change during a reversible process at constant temperature.

$ riangle T$ vs. $T$ (Celsius vs. Kelvin)

$ riangle T$ can be the same in Celsius and Kelvin, but absolute temperature ($T$) must always be in Kelvin.

Q > 0

Heat is added to the system (Net heat in).

Q < 0

Heat is expelled from the system (Net heat out).

Critical Sign Convention for First Law

Work ($W$) is work done ON the system according to the College Board.

Work Calculation in Adiabatic Process

If $Q=0$, then $ riangle U = W$ for a process with no heat transfer.

All Real Engines Efficiency

No real engine can be 100% efficient ($e < 1$); waste heat $Q_C$ can never be zero.

Microstates

Different arrangements of molecules in a system which contribute to the system's entropy.

First Law Equation

Mathematical statement $ riangle U = Q + W$, relating changes in internal energy to heat and work.

Misunderstanding Cycle Area

The area under a PV curve represents work done, not heat; heat must be calculated using the First Law.