Engineering Equations Online Calculator

Kappa, Gas Constant and Specific Heat Values

Gas	Gas	Kappa [/]	Gas Constant [J/kg*K]	Specific Heat [J/kg*K]
Air		1.4	286.7	1,004
Ammonia	NH3	1.3	488.2	2,092
Argon	Ar	1.67	208.1	519
Carbon Dioxide	CO2	1.28	188.9	845
Carbon Monoxide	CO	1.4	296.8	1,042
Helium	He	1.66	2,078.5	5,200
Hydrogen	H2	1.4	4,124	14,350
Methane	CH4	1.32	518.2	2,223
Nitrogen	N2	1.4	296.9	1,038
Oxygen	O2	1.4	259.8	916
Water Vapor	H2O	1.33	188.5	1,690

Here are some of the basic engineering formulas/equations related to energy conversion systems which are built into the Engineering Software product line:

Continuity Equation

m = vA

Momentum Equation

F = (vm + pA)_{out - in}

Energy Equation

Q - W = ((h + v²/2 + gh)m)_{out - in}

State Equation for Ideal Gas

pv = RT/MW

Perfect Gas

c_p = constant

k = c_p / c_v

Isentropic Compression

T₂ / T₁  =  (p₂ / p₁)^(k-1)/k

T₂ / T₁  =  (V₁ / V₂)^(k-1)

p₂ / p₁  =  (V₁ / V₂)^k

Combustion

h_reactants  =  h_products

Isentropic Expansion

T₁ / T₂  =  (p₁ / p₂)^(k-1)/k

T₁ / T₂  =  (V₂ / V₁)^(k-1)

p₁ / p₂  =  (V₂ / V₁)^k

Sonic Velocity

vs  =  (kRT/MW) ^1/2

Mach Number

M =  v/vs

Isentropic Flow

T_t / T  =  (1 + M²(k - 1)/2)

p_t / p  =  (1 + M²(k - 1)/2)^k/(k-1)

h_t  =  (h + v²/2)

T_t  =  (T + v²/(2c_p))

Thrust

Thrust =  vm + (p - p_a)A

Cycle Efficiency

Cycle Efficiency =  Net Work/Heat

Carnot Cycle Efficiency

Carnot Cycle Efficiency =  1 - T_{heat rejection} / T_{heat addition}

Brayton Cycle Efficiency

Brayton Cycle Efficiency =  1 - 1/(p₂ / p₁)^{(k-1)/ k}

Otto Cycle Efficiency

Compression Ratio = V₁ / V₂

Otto Cycle Efficiency =  1 - 1/Compression Ratio^(k-1)

Diesel Cycle Efficiency

Compression Ratio (CR) = V₁ / V₂

Cut-Off Ratio (COR) = V₃ / V₂

Diesel Cycle Efficiency =  1 - (COR^k - 1)/(k*CR^(k-1) *(COR - 1)) 

Fuel Cell

Fuel Cell Efficiency =  - (G_out - G_in)/HHV

Heat Rate

Heat Rate = (1/Cycle Efficiency)*3,412

Physical Properties

For each reaction species, the thermodynamic functions specific heat, enthalpy and entropy
as functions of temperature are given in the form of least squares coefficients as follows:

Cp/R = A1 + A2T + A3T² + A4T³ + A5T⁴

H/(R*T) = A1 + A2T/2 + A3T²/3 + A4T³/4 + A5T⁴/5 + A6/T

S/R = A1lnT + A2T + A3T²/2 + A4T³/3 + A5T⁴/4 + A7

or

S/R = A1lnT + A2T + A3T²/2 + A4T³/3 + A5T⁴/4 + A7 - lnp

For each species, two sets of coefficients are included for two adjecent temperature intervals, 273 to 1,000 [K]
 and 1,000 to 5,000 [K]. The data have been constrained to be equal at 1,000 [K].

Also,

U = H - p*v*MW or U = H - R*T

G = H - S*T

and

u = h - p*v or u = h - R*T/MW

g = h - s*T

Legend:

Cp -- Specific Heat [kJ/kmol*K]

cp -- Specific Heat [kJ/kg*K]

MW -- Molecular Weight [kg/kmol]

R -- Universal Gas Constant [kJ/kmol*K]

Gas Constant = R/MW [kJ/kg*K]

H -- Enthalpy [kJ/kmol]

h -- Enthalpy [kJ/kg]

T -- Temperature [K]

S -- Entropy [kJ/kmol*K]

s -- Entropy [kJ/kg*K]

p -- Pressure [atm]

U -- Internal Energy [kJ/kmol]

u -- Internal Energy [kJ/kg]

V -- Volume [m^3]

v -- Specific Volume [m^3/kg]

G -- Gibbs Free Energy [kJ/kmol]

g -- Gibbs Free Energy [kJ/kg]