Comprehensive Guide to Thermodynamics and Fluids

Ideal Gas

A theoretical gas composed of many randomly moving point particles not subject to interparticle interactions.

Ideal Gas Law

The equation relating pressure, volume, temperature, and number of moles: PV = nRT.

Pressure (P)

The force applied perpendicular to the surface of an object per unit area.

Volume (V)

The amount of space that a substance (solid, liquid, gas, or plasma) occupies.

Universal Gas Constant (R)

A constant used in the ideal gas law, approximately equal to 8.31 J/(mol·K).

Temperature (T)

A measure of thermal energy; must be expressed in Kelvin in gas equations.

Boltzmann’s constant (k_B)

A physical constant relating energy at the individual particle level to temperature, 1.38 × 10^−23 J/K.

Kinetic Molecular Theory (KMT)

A theory that explains the macroscopic properties of gases based on the motion of individual molecules.

Elastic Collisions

Collisions in which total kinetic energy is conserved.

Thermal Equilibrium

Condition where two systems in contact do not exchange heat because they are at the same temperature.

Heat (Q)

The transfer of energy due to a temperature difference.

Conduction

Heat transfer through direct contact via molecular collisions.

Convection

Heat transfer through the bulk movement of fluids.

Radiation

Heat transfer via electromagnetic waves, requiring no medium.

Thermal Conductivity (k)

A measure of a material's ability to conduct heat, expressed in W/(m·K).

Internal Energy (U)

The total energy contained within a system due to its temperature and state.

First Law of Thermodynamics

The principle stating that energy cannot be created or destroyed, only transformed: ΔU = Q + W.

Work (W)

The energy transfer due to a force acting over a distance; in thermodynamics, work done on a gas.

Isothermal Process

A thermodynamic process that occurs at a constant temperature.

Adiabatic Process

A process in which no heat is exchanged with the environment.

Isochoric Process

A process that occurs at constant volume.

Isobaric Process

A process that occurs at constant pressure.

Maxwell-Boltzmann Distribution

A statistical distribution of speeds of particles in a gas, showing the relationship between speed and temperature.

Heat Engine

A device that converts heat energy into work.

Carnot Cycle

Theoretical ideal cycle for a heat engine that provides the maximum possible efficiency.

Entropy (S)

A measure of the disorder or randomness in a system.

Thermal Efficiency (e)

The ratio of useful work output to the total heat input for a thermodynamic process.

Zeroth Law of Thermodynamics

If two systems are in thermal equilibrium with a third system, they are in equilibrium with each other.

PV Diagram

A graph depicting the pressure versus volume of a thermodynamic system.

Kinetic Energy (K)

The energy possessed by an object due to its motion; for molecules, given as K = (1/2)m v^2.

Root-Mean-Square Velocity (v_{rms})

The square root of the average of the squares of the velocities of gas particles.

Compression Work (W)

Work done on the gas, which is positive; occurs when the volume decreases.

Expansion Work

Work done by the gas as it expands, which is negative; occurs when volume increases.

Thermal Conductivity Equation

Q/Δt = (kAΔT)/L; describes the rate of heat transfer through a conductor.

Sign Convention for Q

Positive when heat is added to the system, negative when heat is removed.

Sign Convention for W

Positive when work is done on the system, negative when work is done by the system.

Change in Internal Energy (ΔU)

The change in energy of a system due to heat and work interactions.

Microstates

Different arrangements of particles corresponding to the same macrostate of a thermodynamic system.

Thermodynamic System

A quantity of matter or a region in space chosen for analysis in thermodynamics.

Irreversible Process

A process that cannot be reversed to restore the system and its surroundings to their original conditions.

Equilibrium Conditions

A state where all acting influences are balanced, resulting in no net change.

Law of Conservation of Energy

Energy cannot be created or destroyed; it can only change forms.

Q = mcΔT

Heat transfer equation where m = mass, c = specific heat, and ΔT = change in temperature.

System

The portion of the universe that is under investigation.