SUMMARY OF EQUATIONS FOR PERFECT GASES UNDERGOING NON-FLOW PROCESSES
Q – W = U2 – U1
pV = mRT
Type of process
p, V, T relationships
Constant volume
V1 = V2
V=C
p1 / T1 = p2 / T2
Constant pressure
p1 = p2
p=C
V1 / T1 = V2 / T2
Constant
temperature
Isothermal
p1V1 / T1 = p2V2 / T2
R = cp - cv
γ = cp / cv
Q
W
U2 – U1
mcv(T2 – T1)
Zero
mcv(T2 – T1)
p(V2 – V1)
mcp(T2 – T1)
or
mcv(T2 – T1)
mR(T2 – T1)
p1V1ln(V2 / V1)
T1 = T2
=W
p1V1 = p2V2
or
mRTln(V2 / V1)
Zero
T=C
General polytropic
pVn = C
p1V1 / T1 = p2V2 / T2
(p1V1 – p2V2) / (n – 1)
W + (U2 –
U1 )
p1V1n = p2V2n
T2 /T1 = (p2 / p1)(n-1)/n = (V1 / V2)n-1
1
or
mR(T1 – T2) / (n – 1)
mcv(T2 – T1)
p1V1 / T1 = p2V2 / T2
(p1V1 – p2V2) / (γ– 1)
Adiabatic process
p1V1γ = p2V2γ
pVγ = C
T2 /T1 = (p2 / p1)(γ-1)/γ = (V1 / V2)γ-1
THE STEADY FLOW ENERGY EQUATION
Q – W = mg(Z 2 –Z 1 ) + ½m(C 2 2 - C 1 2 ) + (H 2 – H 1 )
Or expressed in the preferred per-kg or specific energies:
q – w = g(Z 2 –Z 1 ) + ½(C 2 2 - C 1 2 ) + (h 2 – h 1 ) for a mass of 1kg
H 2 – H 1 = mc p (T 2 - T 1 ) for all gas processes
2
Zero
mcv(T2 – T1)
or
mR(T1 – T2) / (γ– 1)
=-W
Or in the preferred specific enthalpy form:
h 2 – h 1 = c p (T 2 - T 1 ) for a mass of 1kg
3