Formulas Thermo

Closed Systems First Law

Sign convention first law

Work by system positive

Heat to system positive

Mass entering system positive

Function Restriction Process Boundary work Boundary work per unit mass

P = f(V) none Prescribed function

PV0 = c n = 0 Constant pressure

PV1 = c

n = 1 Constant temperature

= c

Constant volume Wb = 0 wb = 0

= c

Polytropic

= c

Polytropic

= c

Polytropic

= c

Polytropic

= c

Adiabatic

n = k Isentropic

Work Type Work Work rate Work per unit mass

Potential

Kinetic

Shaft Wsh =2nT

Electrical

Transfer of mass and energy across a system boundary

Open system Closed system Isolated system

Heat Yes Yes No

Work Yes Yes No

Mass Yes No No

Mixed region

Saturated vapour

v = vf + x vfg vg= vf + vfg

u = uf + x ufg ug= uf + ufg

h = hf + x hfg hg= hf + hfg

Subcooled region Mixed region Superheated region

v < vf vf < v < vg v > vg

h < hf hf < h < hg h > hg

u < uf uf < u < ug u > ug

solid liquid Ideal gas

du = Cv dT du = Cv dT du = Cv dT

dh = Cp dT dh = Cp dT dh = Cp dT

Cp = Cv = C

h = u + Pv Cp = Cv = C

h = u + Pv Cp = Cv + R

h = u + Pv

k = Cp/Cv

No restriction No restriction Ideal gas

Variable Symbol Unit Alternative Used in

Acceleration a m/s2 F = ma

Area A m2 V = A ds

Velocity

m/s

Flow rate

kg/s

Force F N kg m/s2 P = F/A

Internal Energy/unit mass u kJ/kg e = u + ke + pe

Internal Energy U kJ kN s E = U + KE + PE

Temperature T K oC Pv=RT

Pressure P kPa kN/m2

Density

kg/m3

Specific volume

m3/kg

Heat Capacity Cv, Cp, C kJ/kgoC dh = u + Pv

Gravity g m/s2 g = 9.81 m/s2

Mass fraction x x = mv/m

Mass m kg w=W/m

Enthalpy H kJ H = U + PV

Enthalpy per unit mass h kJ/kg h = u + Pv

Universal gas constant Ru kJ/kmol K Ru = 8.314 kJ/kmol K

Gas constant R kJ/kg K R = Ru/M

Molecular weight M kg/kmol m=MN

Work W kJ

Work per unit mass w kJ/kg

Rate of work (Power)

kW kJ/s

Heat Q kJ

Heat per unit mass q kJ/kg

Heat transfer rate

kW kJ/s

Number of moles N kmol m=MN

Heat of fusion hif kJ/kg Q=mhif

Heat of vaporization hfg kJ/kg Q=mhfg

Volume V m3 V=vm

Volumetric flow rate

m3/s l/s

Open Systems, Steady State, First Law

Nozzle W = 0

Q = 0 h to ke

Check units: h (kJ/kg) and Vel in m2/s2 = J/kg (factor = 1000)

Diffuser W = 0

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