# All Thermodynamics Formulas List

## Heat Flow

##### Formula Used:

Calculated Heat Flow=(Conductivity of Material*Area(ft2)*(Temperature of Hot Surface(F)-Temperature of Cold Surface(F))/Thickness(inches))

P = ε σ A T4
A = 4 π r2

where,
ε - Emissivity
A - Surface area
T - Temperature

## Otto Cycle Compression Ratio (CR)

#### Formula:

CR = v1/v2

Where,

V1 = Voltage1
V2 = Voltage2
CR = Compression Ratio

## Carnot Cycle Efficiency (�?)

#### Formula :

ƞ = 1 - (TC / TH)

Where,
ƞ = Carnot Efficiency
TC = Absolute Temperature of the Cold Reservoir
TH = Absolute Temperature of the Hot Reservoir

## Stefan–Boltzmann Law - Radiant Heat Energy

#### Formula Used:

E α T4 or E = σ T4

Where,

σ = Stefan's constant ( 5.67 × 10-8 W m-2 K-4)
T = Absolute Temperature

## SWG to MM Conversion

#### Formula:

in = mm / 25.4,
cmm = PI * ( mm / 2 )2,
cin = PI * ( mm / 50.8)2,

Where,

in is the size of the wire in inches,
mm is the size of the wire in mm,
cmm is the cross sectional area in mm,
cin is the cross sectional area in inches.
The value of mm is found from this

qx=KT*(ΔT/x)

## Thermal Linear and Volumetric Expansion

#### Thermal Linear and Volumetric Relationship Expansion:

Thermal Volumetric Expansion Coefficient: Thermal Linear Expansion Coefficient: where,
b = Thermal Volumetric Expansion Coefficient,
a = Thermal Linear Expansion Coefficient.

## Thermal Volumetric Expansion Coefficient

#### Thermal Volumetric Expansion:

Thermal Volumetric Expansion Coefficient: Initial Volume: Final Volume: Initial Temperature: Final Temperature: where,

b = Thermal Volumetric Expansion Coefficient,

Vi = Initial Volume,

Vf = Final Volume,

Ti = Initial Temperature,

Tf = Final Temperature.

## Thermal Linear Expansion Coefficient

#### Thermal Linear Expansion:

Thermal Linear Expansion Coefficient: Initial Length: Final Length: Initial Temperature: Final Temperature: where,
a = Thermal Linear Expansion Coefficient,
Li = Initial Length,
Lf = Final Length,
Ti = Initial Temperature,
Tf = Final Temperature,

## Thermal Diffusivity

#### Thermal Diffusivity:

Thermal Diffusivity: Thermal Conductivity: Density: Specific Heat Capacity: where,
α = Thermal Diffusivity,
k = Thermal Conductivity,
ρ = Density,
cp = Specific Heat Capacity.

## Thermal Conductivity

#### Thermal Conductivity:

Heat Transfer Rate or Flux: Thermal Conductivity Constant: Temperature Differential: Distance or Length: where,

qx = Heat Transfer Rate or Flux,

KT = Temperature Differential,

ΔT = Thermal Conductivity Constant,

x = Distance or Length.

## Hall Voltage

#### Formula:

Vh = RhBzIz / w

Where,

Vh = Hall Voltage in a Rectangular Strip
Rh = Hall Coefficient
Bz = Magnetic Flux Density
Iz = Applied Current
w = Strip Thickness

## Ehrenfest Equation for Second Order Phase Transition

#### Formula:

dp/dT=(βp2p1)/(KT2-KT1)

Where,

βp2p1 = Isobaric Expansivity
KT1,KT2= Isothermal compressibility
dp/dT = Ehrenfest equation for Second Order Phase Transition

## Ehrenfest Equation for First Order Phase Transition

#### Formula:

dp/dT=(1/VT) ((Cp2-Cp1)/(Bp2-Bp1))

Where,

V = Volume
T = Temperature of phase change
Cp1,Cp2 = heat capacity
Bp1,Bp2 = Isobaric expansivity
dp/dT = Ehrenfest Equation for First Order Phase Transition

## Van der Waals Force (Interaction)

#### Formula:

f=(-3/4)*[(a2*h*w)/(4*π*e)2*r6]

Where,

a=Particle Polarisability
h=Planck Constant / 2π
w=Angular Frequency of Polarised Orbital
e=Permittivity of Free Space
f=Van der Waals Interaction
r=Particle Separation

## Log Mean Temperature Difference (LMTD)

#### Formula : ## Heat Transfer (Q)

#### Formula Used:

Q = mL

Where

Q = Heat Transferred to a System
m = Mass of sample
L = Heat of Transformation

## Flow Coefficient (Cv) for Saturated Wet Steam

#### Formula:

ζ = ws / (ww + ws)
Cv = Cv_saturated * ζ1/2

Where,

Cv = Flow Coefficient Saturated Wet Steam
Cv_saturated = Saturated Flow Coefficient
ζ = Dryness Fraction
ww = Mass of Water
ws = Mass of Steam

## Solar Panel Capacity

#### Formula:

Inverter capacity = Number of panel x Watts per panel
Battery charge time = Inverter capacity / Battery volts

## Solar Panel Requirement

#### Formula:

Number of Solar Panel = ( ( Total Energy * natural system losses ) / Solar Hours ) / Solar Panel Watts

Where,

natural system losses = 1.2 (this factor allows for natural system losses, assuming 85% efficiency)
Total Energy = Appliances watts * Appliances usage hours/day

## Van der Waals Gas Critical Pressure

#### Formula:

Pc = a/27b2

Where,

Pc=Critical Pressure
a,b=Van Der Waals Constant

## Dieterici Gas Critical Pressure

#### Formula:

p=a/4b2e2

Where,

Pc=Critical Pressure
a,b=Dieterici Constants

## Dieterici Gas Reduced Pressure

#### Formula:

Pr=(Tr/2Vr-1)exp(2- (2/VrTr))

Where,

Pr=Reduced Pressure
Tr=Reduced Temperature
Vr=Reduced Volume

## Gas Viscosity

#### Formula:

n=(1/2)plc

Where,

n=Dynamic Viscosity
p=Density
l=Mean Free Path
c=Mean Molecular Speed

#### Formula :

M = (1 - A) × σ T 4

Where,

M = Exitance
A = Albedo
σ = Stefan - Boltzmann Constant
T = Temperature

## Reduced Van der Waals Equation of State

#### Formula:

Tr = ((Pr+3/Vr2)(3Vr-1))/8

Where,

Tr=Reduced Temperature
Pr=Reduced Pressure
Vr=Reduced Volume

## Critical Molar Volume of Van Der Waals Gas

#### Formula

Vmc = 3*b

Where,

Vmc=Critical Molar Volume
b=Van Der Waals Constant

## Van der Waals Gas Critical Temperature

#### Formula

Tc = 8a / 27 Rb

Where,

Tc=Critical Temperature
a,b=Van Der Waals Constants
R=Molar Gas Constant

## Critical Molar Volume of Dieterici Gas

#### Formula

Vmc = 2b'

Where,

Vmc=Critical Molar Volume
b'=Dieterici Constant

## Mean Free Path

#### Formula:

l = 1 / ( √( 2 ) * πd2n )

Where,

l=Mean Free Path of Transport Properties
d=Molecular Diameter
n=Particle Number Density

## Dieterici Gas Equation of State Pressure

#### Formula

p = RT / Vm-b'exp(-a' / RTVM)

Where,

p = Pressure
r = Molar Gas Constant
t = Temperature
v = Molar Volume
a',b' = Dieterici Constants

## Flow Coefficient of Air

#### Formula:

Cv = (q [SG (T + 460)]1/2) / (660 * pi)

Where,

Cv = Flow Coefficient for Air and Other Gases
q = Free Gas / Standard Cubic Feet Per Hour
SG = Specific Gravity
T = Gas Temperature
pi = Inlet Gas Absolute Pressure

## Specific Latent Heat

#### Formula:

L = Q / m

Where,

L = Specific Latent Heat
Q = Energy in Heat
m = Mass

MA = l / e
l = MA * e
e= l / MA

Where,

e = Effort

## Monatomic Gas Pressure

#### Formula:

p=(1/3)*n*m*c2

Where,

n = Number density
m = Particle mass
p = Pressure
c2 = mean squared particle velocity

## Fermi Energy of Fermi Gas

#### Formula:

EF = (h2 / 2me) * (3π2n)2/3

Where,

EF = Fermi energy
h = Planck constant/2π
me = Electron mass
n = Number of electrons per unit volume

## Fermi Temperature of Electrons

#### Formula:

TF=(EF/kB)

Where,

TF = Fermi Temperature of Electrons
EF = Fermi Energy
kB = Boltzmann Constant

## Fermi Gas Electron Heat Capacity

#### Formula:

Cv=((π2kB2)/(2EF))*T

Where,

Kb = Boltzmann constant
EF = Fermi energy
T = Temperature
Cv = Heat capacity per electron

## Density of States of Fermi Gas

#### Formula:

g = v/2π2(2*m / h2)3/2*e1/2

Where,

g = Density of states
m = Electron mass
h = Planck constant
e = Electron energy
v = Gas volume

## Phase Transition Latent Heat

#### Formula:

l=T×(p-r)

Where,

l=Heat Absorbed
T=Temperature of Phase Change
p=Entropy (S1)
r=Entropy (S2)

## Clausius Clapeyron Relation

#### Formula:

P = (S2 - S1) / (V2 - V1)

Where,

S2 = Entropy
S1 = Entropy
V2 = Volume
V1 = Volume
P = Slope of Tangent using Clausius Clapeyron

## Phonon Lattice Thermal Conductivity

#### Formula:

λ=(1/3)*(Cv/vs)l

Where,

λ = Thermal conductivity
Cv = Lattice heat capacity
V = Volume
vs = Effective sound speed
l = Phonon mean free path

## Internal Energy of Monatomic Gas

#### Formula:

U = (3/2)(NkT)

Where,

U = Internal Energy of Monatomic Gas
N = Number of Particles
k = Boltzmann Constant
T = Temperature

## Flow Coefficient of Air and Gases for Non-Critical Pressure Drop

#### Formula:

dp = (pi - po)
Cv = (q [SG (T + 460)]1/2)/ [1360 (dp * po)(1/2)]

Where,

Cv = Flow Coefficient for Air and Other Gases
q = Free Gas / Standard Cubic Feet Per Hour
SG = Specific Gravity
T = Gas Temperature
pi = Inlet Gas Absolute Pressure
po = Outlet Gas Absolute Pressure
dp = Pressure Drop

## Convective Heat Transfer

#### Formula:

Heat Transferred = hc × A × dT

Where,

A = Heat Transfer Area of the Surface
hc = Convective Heat Transfer Coefficient
dT = Temperature Difference Between the Surface and Bulk Fluid

## Isentropic Flow Pressure Relation Based on Temperature

#### Formula:

P / Pt = (T / Tt)(γ / γ - 1)

Where,

P / Pt = Isentropic Flow Relation Between Pressure and Total Pressure
P = Pressure
Pt = Total Pressure
T = Temperature
Tt = Total Temperature
γ = Specific Heat Ratio

## Mean Heat Transfer Rate of Heat Exchanger

#### Formula:

q = (cp * dT) * (m/t)

Where,

q = Mean Transfer Rate of Heat Exchanger
dT = Change in Temperature
cp = Specific Heat Capacity
m/t = Mass Flow Rate of Product (m = mass, t = time)

## Most Probable Speed in Maxwell Boltzmann Distribution

#### Formula:

c = (2kT / m)1/2

Where,

k = Boltzmann Constant
T = Temperature
c = Most Probable Speed in Maxwell Boltzmann Distribution
m = Particle mass

## Kirchhoff's Law Radiative Transfer to Find Source Function

#### Formula:

Sv = jv / αv

Where,

Sv = Source Function using Kirchhoff Law in Radiative Transfer
jv = Specific Emission Coefficient
αv =Absorption coefficient

## Heat

#### Formula:

Q = CpmΔT

Where,

Q = Heat
Cp = Specific Heat
m = Mass
ΔT = Change in Temperature

## Sensible Heat

#### Formula:

Q = M × C × T

Where,

Q = Sensible Heat
M = Mass of the Body
C = Specific Heat Capacity
T = Change of the Temperature

## Heat Capacity Ratio

#### Formula:

γ = Cp / Cv

Where,

γ = Heat Capacities Ratio
Cp = Heat Capacity at Constant Pressure
Cv = Heat Capacity at Constant Volume

## Oil Recovery Factor

#### Formula:

Oil Recovery Factor = Estimate Of Recoverable Oil / Estimate Of In Place Oil