Functions§
- adiabatic_
final_ pressure - Adiabatic relation: P1 * V1^γ = P2 * V2^γ → P2 = P1 * (V1/V2)^γ
- average_
kinetic_ energy - Average kinetic energy of a gas molecule: KE = (3/2) * k_B * T
- biot_
number - Biot number: Bi = hL/k (external convection vs internal conduction)
- boiling_
point_ elevation - Boiling point elevation: ΔTb = Kb × m
- carnot_
efficiency - Carnot efficiency: η = 1 - T_cold / T_hot
- celsius_
to_ fahrenheit - Celsius to Fahrenheit: F = C × 9/5 + 32
- celsius_
to_ kelvin - Celsius to Kelvin: K = C + 273.15
- celsius_
to_ rankine - Celsius to Rankine: R = (C + 273.15) × 9/5
- clausius_
clapeyron - Clausius-Clapeyron (approximate): ln(P2/P1) = (L/R) * (1/T1 - 1/T2) Returns P2 given P1, T1, T2, and molar latent heat L.
- convective_
heat_ rate - Newton’s law of convection: Q/t = h×A×ΔT
- cop_
heat_ pump - Coefficient of performance (heat pump): COP = Q_hot / W
- cop_
refrigerator - Coefficient of performance (refrigerator): COP = Q_cold / W
- entropy_
change_ ideal_ gas - Entropy change for an ideal gas: ΔS = nCvln(T2/T1) + nRln(V2/V1)
- entropy_
change_ isothermal - Entropy change for heat transfer at constant temperature: ΔS = Q / T
- fahrenheit_
to_ celsius - Fahrenheit to Celsius: C = (F - 32) × 5/9
- fahrenheit_
to_ kelvin - Fahrenheit to Kelvin via Celsius
- freezing_
point_ depression - Freezing point depression: ΔTf = Kf × m
- grashof_
number - Grashof number: Gr = gβΔTL³/ν²
- heat_
conduction_ rate - Heat conduction (Fourier’s law): Q/t = k * A * ΔT / d
- heat_
equation_ stability - Maximum stable time step for explicit finite difference: dt_max = dx²/(2α)
- heat_
equation_ step_ 1d - Explicit finite difference: T_i^(n+1) = T_i^n + α×dt/dx² × (T_(i+1) - 2T_i + T_(i-1)) Fixed boundary conditions (first and last elements unchanged).
- heat_
of_ vaporization_ trouton - Trouton’s rule: ΔHvap ≈ 88 × Tb (J/mol)
- heat_
radiation_ power - Heat radiation (Stefan-Boltzmann law): P = ε * σ * A * T^4
- heat_
transfer - Heat transfer: Q = m * c * ΔT
- ideal_
gas_ moles - Number of moles: n = PV / (RT)
- ideal_
gas_ pressure - Ideal gas law: PV = nRT. Solve for pressure: P = nRT / V
- ideal_
gas_ temperature - Solve for temperature: T = PV / (nR)
- ideal_
gas_ volume - Solve for volume: V = nRT / P
- kelvin_
to_ celsius - Kelvin to Celsius: C = K - 273.15
- kelvin_
to_ fahrenheit - Kelvin to Fahrenheit via Celsius
- latent_
heat - Heat for phase change: Q = m * L (latent heat)
- mean_
free_ path - Mean free path: λ = 1 / (√2 * π * d^2 * n/V)
- net_
radiation_ power - Net radiative heat transfer: P = ε * σ * A * (T_hot^4 - T_cold^4)
- newton_
cooling - Newton’s law of cooling: dT/dt = -k * (T - T_env) Returns temperature at time t: T(t) = T_env + (T0 - T_env) * e^(-k*t)
- nusselt_
number - Nusselt number: Nu = hL/k
- prandtl_
number - Prandtl number: Pr = ν/α
- quality
- Steam quality (dryness fraction): x = m_vapor / m_total
- radiative_
equilibrium_ temperature - Radiative equilibrium temperature: T = ((L(1-a))/(16πσd²))^(1/4)
- rankine_
to_ celsius - Rankine to Celsius: C = R × 5/9 - 273.15
- rayleigh_
number - Rayleigh number: Ra = Gr × Pr
- rms_
speed - RMS speed of gas molecules: v_rms = sqrt(3 * k_B * T / m)
- saturation_
pressure - Antoine equation: log10(P) = A - B/(C+T), returns P
- specific_
enthalpy_ wet - Specific enthalpy of wet steam: h = hf + x × hfg
- spectral_
exitance - Planck’s law: M = (2πhc²/λ⁵) × 1/(e^(hc/λkT) - 1)
- subcool_
degree - Degree of subcooling: ΔT = T_sat - T_actual
- superheat_
degree - Degree of superheat: ΔT = T_actual - T_sat
- thermal_
diffusivity - Thermal diffusivity: α = k/(ρ×cₚ)
- thermal_
efficiency - Thermal efficiency: η = W / Q_hot
- wien_
displacement - Wien’s displacement law: λ_max = b/T where b = 2.898e-3 m·K
- work_
adiabatic - Work done during adiabatic process: W = (P1V1 - P2V2) / (γ - 1)
- work_
isobaric - Work done during isobaric (constant pressure) process: W = P * ΔV
- work_
isothermal - Work done by an ideal gas during isothermal expansion: W = nRT * ln(V2/V1)