Carnot Cycle Lab

Class XI/XII · Thermodynamics: the most efficient heat engine, on a PV diagram.

Controls

Hot reservoir Tₕ600 K

Cold reservoir T_c300 K

Initial volume V_A1.00 m³

Isothermal ratio V_B/V_A2.00

Live readouts (n = 1 mol)

Q_H absorbed3458 J

Q_C rejected1729 J

W = Q_H − Q_C1729 J

η = W / Q_H50.00 %

η (Carnot)50.00 %

V_C / V_D2.000

Formula

Carnot cycle (n moles, ideal gas):
  Isothermal: PV = nRT
  Adiabatic:  PV^γ = const,  TV^(γ−1) = const

  Q_H = nR Tₕ ln(V_B/V_A)
  Q_C = nR T_c ln(V_C/V_D)
  W   = Q_H − Q_C
  η   = 1 − T_c/Tₕ

Note: V_B/V_A = V_C/V_D from the two adiabats.

Try this: Pin Tₕ at 600 K and slide T_c from 300 → 100 K: η climbs as 1 − T_c/Tₕ. Try the three γ toggles: the adiabats steepen with γ, but η is still 1 − T_c/Tₕ — Carnot efficiency depends only on the reservoirs, not the working substance.

Carnot Cycle Lab

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