Thermodynamics 1 Equations Flashcards
Sign Convention for Heat
Heat IN is +ive
Sign Convention for Work
Work OUT is +ive
Displacement Work
W = int P dV
Isothermal PV relationship
P V = m R T
Isentropic PV relationship
P V^γ = k
First Law of Thermodynamics
Q - W = ΔU (for a closed system)
Enthalpy Definition
h = u + P v
Ideal Gas Law
P v = R T
Specific Heat (constant volume)
Cv = du/dT
Change in u
u2 - u1 = Cv * ( T2 - T1 )
Specific Heat (constant pressure)
Cp = dh/dT
Change in h
h2 - h1 = Cp * ( T2 - T1 )
Specific Heat Relationship
R = Cp - Cv
γ in terms of specific heats
γ = Cp / Cv
Dryness fraction from specific volume
x = (v - vf) / (vg - vf)
Dryness fraction from specific enthalpy
x = (h - hf) / (hg - hf)
Dryness fraction from specific entropy
x = (s - sf) / (sg - sf)
Specific enthalpy h_fg for wet steam
hfg = hg - hf
Specific enthalpy h of wet steam
h = hf + x * hfg
Heat (Q) and Temp (T) relationship for a reversible heat engine
Qh / Th = Qc / Tc
Reversible Heat Temp relationship (condition)
int dQ/T = 0
Irreversible Heat Temp relationship condition
int dQ/T < 0
Entropy Definition
dS = dQ(rev) / T
Change in Entropy
S2 - S1 = int dQ(rev)/T
Reversible change in Entropy
S2 - S1 = int dQ / T
Irreversible change in Entropy
S2 - S1 > int dQ / T
1st T ds Equation
T ds = du + P dv
2nd T ds Equation
T ds = dh - v dP
Integrated T ds equation in T and v
s2 - s1 = Cv ln(T2/T1) + R ln(v2/v1)
Integrated T ds equation in T and P
s2 - s1 = Cp ln(T2/T1) - R ln(P2/P1)
Integrated T ds equation in P and v
s2 - s1 = Cp ln(v2/v1) + Cv ln(P2/P1)
Isentropic T v relationship
T * v^(γ - 1) = k
Isentropic T P relationship
T / P^((γ-1)/γ) = k
Isentropic Efficiency (ηs) for a turbine
ηs = (h1 - h2) / (h1 - h2s)
Isentropic Efficiency (ηs) for a compressor
ηs = (h2s - h1) / (h2 - h1)
Reversible Heat Transfer (Q) from a T s Diagram
Q = int T ds
SFEE
Steady Flow Energy Equation
Qdot- Wdot = mdot(h + 1/2 c^2 + gz)[out] - mdot(h + 1/2 c^2 + gz)[in]
Heat Engine Efficiency for any engine
η = 1 - Qc/Qh
Reversible Heat Engine Efficiency (Carnot Efficiency)
η = 1 - Tc/Th
COP for a Refrigerator
COP = Qc / (Qh - Qc)
COP for a Reversible Refrigerator
COP(rev) = Tc / (Th - Tc)
COP for a Heat Pump
COP = Qh / (Qh - Qc)
COP for a Reversible Heat Pump
COP(rev) = Th / (Th - Tc)
