Thermodynamic Terms

Reference data and engineering information about thermodynamic terms for miscellaneous applications.

thermodynamicterms

Overview

Engineering reference data for Thermodynamic Terms in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Symbol	Description	Unit
$x$	Input value	—
$y$	Output value	—
$k$	Conversion factor	—

Thermodynamic terms and their associated functions.
Term	Function
Activity coefficient	$γ_i = \frac{f_i}{x_i f_i^θ}$
Chemical potential	$μ_i = \left(\frac{\partial G}{\partial n_i}\right)_{T,p,n_{j≠i}}$
Energy	$U$
Enthalpy	$H = U + pV$
Entropy	$S$
Fugacity	$f_i = x_i \exp\left\{\frac{μ_i - μ_i^{ig}}{RT}\right\}$
Gibbs (free) energy	$G = U + pV - TS$
Gibbs-Duhem relation	$0 = SdT - Vdp + \sum_i n_i dμ_i$
Gibbs-Helmholtz equation	$H = G - T\left(\frac{\partial G}{\partial T}\right)_p$
Helmholtz energy	$A = U - TS$

Thermodynamic Definitions

Energy Forms

Chemical Energy: Related to molecular relationships in compounds. Releases heat in exothermic reactions; absorbs heat in endothermic reactions.
Electric Energy: Associated with electron flow through a conductor.
Kinetic Energy: Energy of motion, proportional to mass and the square of velocity.
Nuclear Energy: Energy from atomic relationships, released in fission or fusion.
Potential Energy: Energy of position or location within a force field.

Thermodynamic Properties

Internal Energy: Activity within molecular structure, typically measured by temperature.
Enthalpy: Energy unit combining internal energy with pressure-volume or flow work.
Entropy: Measure of disorder or randomization; always produced in natural processes.
Temperature: Quantifies the warm/cold level of internal energy in a substance.
Heat: Energy in transit due to temperature difference.
Work: Energy transfer equivalent to moving a mass against a force.
Property: A measurable characteristic (e.g., temperature, density, pressure).

Additional Thermodynamic Relations

Heat Capacities

Isobaric heat capacity: $C_p = \left(\\frac{\\partial H}{\\partial T}\\right)_p$
Isochoric heat capacity: $C_V = \left(\\frac{\\partial U}{\\partial T}\\right)_V$
Relation: $C_p - C_V = \\frac{T α^2 V}{κ_T}$

Compressibility & Expansivity

Isobaric expansivity: $α_V = \\frac{1}{V} \\left(\\frac{\\partial V}{\\partial T}\\right)_p$
Isothermal compressibility: $κ_T = - \\frac{1}{V} \\left(\\frac{\\partial V}{\\partial p}\\right)_T$
Isentropic compressibility: $κ_S = - \\frac{1}{V} \\left(\\frac{\\partial V}{\\partial p}\\right)_S$
Relation: $κ_T - κ_S = \\frac{T α_V^2 V}{C_p}$

Joule-Thomson Effects

Joule-Thomson coefficient: $μ_{JT} = \\left(\\frac{\\partial T}{\\partial p}\\right)_H = - \\frac{1}{C_p} \\left[ V - \\left(\\frac{\\partial V}{\\partial T}\\right)_p \\right]$
Φ function: $Φ_{JT} = \\left(\\frac{\\partial H}{\\partial p}\\right)_T = V - T \\left(\\frac{\\partial V}{\\partial T}\\right)_p$

$\\left(\\frac{\\partial S}{\\partial p}\\right)_T = - \\left(\\frac{\\partial V}{\\partial T}\\right)_p$ $\\left(\\frac{\\partial S}{\\partial V}\\right)_T = \\left(\\frac{\\partial p}{\\partial T}\\right)_V$

Ideal Gas Relations

For a perfect gas (denoted by superscript $ig$ ): $pV = \\left(\\sum_i n_i\\right) RT$ $μ_i^{ig} = μ_i^θ + RT \\ln\\left(\\frac{x_i p}{p^θ}\\right)$

References

Original Source

Source: engineeringtoolbox.com