Thermodynamics

PV = const — see hyperbola on PV plot.

PV^γ = const — steeper than isotherm.

V = const, W = 0, Q = ΔU.

P = const, W = PΔV.

ΔU = Q − W — heat in, work out.

W = ∫P dV — area under PV curve, 3 paths.

Rectangular cycle on PV — η = W_net / Q_in.

COP = Q_c / W — work input pulls heat from cold.

η = 1 − T_c/T_h — ideal max efficiency.

Compare side-by-side — losses in real systems.

Switch between 4 processes on a single plot.

Carnot rectangle — area = work done.

ΔU = 0, W = ∮P dV — engine vs refrigerator direction.

U = (f/2) nRT — depends only on T.