1 & 2 - Gas Power and Carnot Cycle

Gas Power Cycle: Thermal Efficiency

n_th = Wnet / Qin = 1- Tl/Th

Carnot PVT Relationships: Process 1-2

T=C (Isothermal expansion / heat addition)

P1V1 = P2V2

P1/P2 = V2/V1 = re_T = isothermal expansion ratio

Carnot PVT Relationships: Process 2-3

S=C (Isentropic Expansion)

V3/V2 = (P2/P3)^(1/K) = (T2/T3)^(1/K-1) = re_s = isentropic expansion ratio

Carnot PVT Relationships: Process 3-4

T=C (Isothermal compression / heat rejection)

P3V3 = P4V4

V3/V4 = P4/P3 = r_kt = isothermal compression ratio

Carnot PVT Relationships: Process 4-1

S=C (Isentropic Compression)

V4/V1 = (P1/P4)^(1/K) = (T1/T4)^(1/K-1) = r_ks = isentropic compression ratio

Carnot: Isentropic Ratio Relation

isentropic expansion ratio = isentropic compression ratio

r_es = r_ks

V3/V2 = V4/V1

Carnot: Isothermal Ratio Relation

isothermal expansion ratio = isothermal compression ratio

r_et = r_kt

V2/V1 = V3/V4

Carnot: Heat Added

Qa = Q1-2 = T1(S2-S1)

Carnot: Heat Rejection

Qr = Q3-4 = T3(S4 - S3) = -T3(S3 - S4) = -T3(S2 - S1)

Carnot Net Work: Wk1-2

Wk1-2 = mRT x ln(V2/V1)

Carnot Net Work: Wk2-3

Wk2-3 = mR(T3-T2) / 1-K

Carnot Net Work: Wk3-4

Wk3-4 = mRT3 x ln(V4/V3)

Carnot Net Work: Wk4-1

Wk4-1 = mR(T1 – T4) / 1-k

Carnot Net Work: Wknet

Wknet = Qa + Qr = (T1 - T3)(S2 - S1)

Carnot: Thermal Efficiency

e = Wnet / Qa = (T1-T3) / T1

e = 1 - T4/T1 = 1-(1/r_ks^(K-1))

e = 1 - T3/T2 = 1-(1/r_es^(K-1))

Carnot: Mean Effective Pressure

Pm = Mep = average working pressure = Wknet / V_D = Wknet / (V3 - V1)

Carnot: Piston Displacement

V_D = V3 - V1 = Vmax - Vmin