Thermodynamics Cheat Sheet

The core ideas of Thermodynamics distilled into a single, scannable reference — perfect for review or quick lookup.

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Quick Reference

Zeroth Law of Thermodynamics

If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This law provides the logical foundation for the concept of temperature and justifies the use of thermometers.

First Law of Thermodynamics

The change in internal energy of a system equals the heat added to the system minus the work done by the system: $\Delta U = Q - W$. This is a statement of conservation of energy applied to thermal processes, where $Q$ is positive when heat flows into the system and $W$ is positive when the system does work on its surroundings.

Second Law of Thermodynamics

The total entropy of an isolated system can never decrease over time. Heat spontaneously flows from hot to cold, never the reverse, without external work. This law establishes the directionality (arrow of time) of natural processes and places fundamental limits on the efficiency of heat engines.

Entropy

A thermodynamic quantity that measures the number of microscopic configurations (microstates) consistent with a system's macroscopic state. In any spontaneous process, the total entropy of the universe increases. Entropy is often associated with disorder, but more precisely it quantifies the dispersal of energy among available microstates.

Ideal Gas Law

The equation of state for an ideal gas: $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the universal gas constant, and $T$ is absolute temperature in kelvins. This law combines Boyle's, Charles's, and Avogadro's laws into a single relationship.

PV Diagrams

Graphical representations of thermodynamic processes plotted with pressure on the vertical axis and volume on the horizontal axis. The area under a curve on a PV diagram equals the work done by the gas during that process, and a closed loop represents a complete thermodynamic cycle.

Heat Engines and Carnot Efficiency

A heat engine is a device that converts thermal energy into mechanical work by cycling a working substance between a hot reservoir and a cold reservoir. The Carnot efficiency, $\eta = 1 - T_C / T_H$, sets the maximum possible efficiency for any engine operating between temperatures $T_H$ and $T_C$ (in kelvins).

Heat Transfer: Conduction, Convection, Radiation

Conduction transfers heat through direct molecular collisions in a material. Convection transfers heat by the bulk movement of a heated fluid. Radiation transfers energy via electromagnetic waves and requires no medium. All three mechanisms can operate simultaneously in real systems.

Internal Energy

The total kinetic and potential energy of all the molecules in a system. For an ideal gas, internal energy depends only on temperature: $U = \frac{3}{2} nRT$ for a monatomic ideal gas. Changes in internal energy are related to heat and work by the first law.

Thermodynamic Processes

Named categories of state changes: isothermal (constant temperature, $\Delta T = 0$), isobaric (constant pressure, $\Delta P = 0$), isochoric (constant volume, $\Delta V = 0$, so $W = 0$), and adiabatic (no heat transfer, $Q = 0$). Each process has characteristic equations relating $P$, $V$, $T$, $Q$, and $W$.

Key Terms at a Glance

Thermodynamics:The branch of physics dealing with heat, work, temperature, and energy, and the laws governing their interconversion.

Entropy:A measure of the number of microstates consistent with a given macrostate; quantifies the dispersal of energy. Symbol: $S$, units: J/K.

Internal Energy:The total kinetic and potential energy of all molecules in a system. For an ideal gas, it depends only on temperature.

Heat Engine:A device that converts thermal energy into mechanical work by operating between a hot and cold reservoir in a cyclic process.

Carnot Cycle:A theoretical thermodynamic cycle consisting of two isothermal and two adiabatic processes. It represents the most efficient possible engine between two temperatures.

Isothermal Process:A thermodynamic process occurring at constant temperature.

Adiabatic Process:A thermodynamic process in which no heat is exchanged between the system and its surroundings ($Q = 0$).

Isobaric Process:A thermodynamic process occurring at constant pressure.

Isochoric Process:A thermodynamic process occurring at constant volume; also called isometric or isovolumetric.

Thermal Equilibrium:The state in which two systems in thermal contact no longer exchange net heat because they are at the same temperature.

PV Diagram:A graph plotting pressure vs. volume for a gas. The area under a process curve represents work; the area enclosed by a cycle represents net work.

Coefficient of Performance (COP):A measure of the effectiveness of a refrigerator or heat pump: $\text{COP}_{\text{ref}} = Q_C / W$ for a refrigerator.

Specific Heat:The amount of heat required to raise the temperature of 1 kg of a substance by 1 K. Symbol: $c$, units: J/(kg K).

Conduction:Heat transfer through direct molecular collisions within a material, driven by a temperature gradient.

Convection:Heat transfer by the bulk movement of a fluid (liquid or gas) due to temperature-driven density differences.

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