Thermodynamic Terms

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 Functions Table

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: $Φ_{JT} = \\left(\\frac{\\partial H}{\\partial p}\\right)_T = V - T \\left(\\frac{\\partial V}{\\partial T}\\right)_p$

Maxwell Relations

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

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