List of All Thermodynamics Formulas

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))

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Stefan Boltzmann Law - Radiation Energy

Formula:


P = ε σ A T4
A = 4 π r2

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

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Otto Cycle Compression Ratio (CR)

Formula:


CR = v1/v2

Where,

V1 = Voltage1
V2 = Voltage2
CR = Compression Ratio

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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

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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)
E = Radiant Energy
T = Absolute Temperature

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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

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Heat Transfer Rate

Formula Used:


qx=KT*(ΔT/x)

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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.

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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.

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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,

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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.

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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.

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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

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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

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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

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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

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Log Mean Temperature Difference (LMTD)

Formula :


LMTD Formula

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Heat Transfer (Q)

Formula Used:


Q = mL

Where

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

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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

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Solar Panel Capacity

Formula:

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

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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

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Van der Waals Gas Critical Pressure

Formula:

Pc = a/27b2


Where,

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

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Dieterici Gas Critical Pressure

Formula:

p=a/4b2e2


Where,

Pc=Critical Pressure
a,b=Dieterici Constants

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Dieterici Gas Reduced Pressure

Formula:

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


Where,

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

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Gas Viscosity

Formula:

n=(1/2)plc


Where,

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

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Black Body Radiation Exitance

Formula :

M = (1 - A) × σ T 4

Where,

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

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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

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Critical Molar Volume of Van Der Waals Gas

Formula

Vmc = 3*b


Where,

Vmc=Critical Molar Volume
b=Van Der Waals Constant

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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

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Critical Molar Volume of Dieterici Gas

Formula

Vmc = 2b'


Where,

Vmc=Critical Molar Volume
b'=Dieterici Constant

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Mean Free Path

Formula:


l = 1 / ( √( 2 ) * πd2n )


Where,

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

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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

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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

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Specific Latent Heat

Formula:

L = Q / m


Where,

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

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Mechanical Advantage

Formula:

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


Where,

MA = Mechanical Advantage
l = Load
e = Effort

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Monatomic Gas Pressure

Formula:

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


Where,

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

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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

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Fermi Temperature of Electrons

Formula:

TF=(EF/kB)


Where,

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

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Fermi Gas Electron Heat Capacity

Formula:

Cv=((π2kB2)/(2EF))*T


Where,

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

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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

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Phase Transition Latent Heat

Formula:

l=T×(p-r)


Where,

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

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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

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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

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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

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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

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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

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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

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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)

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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

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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

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Heat

Formula:

Q = CpmΔT


Where,

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

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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

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Heat Capacity Ratio

Formula:

γ = Cp / Cv


Where,

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

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Oil Recovery Factor

Formula:

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

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