Physic Labs

Thermal physics

Heat engines, efficiency, and the Carnot cycle

Explore the ideal efficiency of a heat engine between a hot reservoir Th and a cold reservoir Tc. Read ηCarnot, maximum work Wmax, and rejected heat Qc; verify η=1−Tc/Th\eta = 1 - T_c/T_h and W=ηQhW = \eta Q_h.

Undergraduate

⚠ For real experiments with hot steam, heated gas, or pressure vessels, wear protection, never open a pressurized container, and keep a safe distance from high-temperature sources.

Equipment

  • Canvas showing the closed p–V cycle and the engine's heat-flow diagram
  • «Nguồn nóng Th» (hot reservoir) slider, 350–900 K
  • «Nguồn lạnh Tc» (cold reservoir) slider, 180–340 K
  • «Nhiệt nhận Qh» (absorbed heat) slider, 100–1000 J
  • Readout line «ηCarnot = …; Wmax = ηQh = …; Qc = Qh − W = …»

Procedure

  1. Measure efficiency vs hot temperature

    Hold «Nguồn lạnh Tc» at 300 K, raise «Nguồn nóng Th» from 350 to 900 K, and record «ηCarnot» at each step. Compute 1−Tc/Th1 - T_c/T_h for each pair and compare with the readout; watch the efficiency approach 100 % without ever reaching it.

  2. Vary the cold reservoir and absorbed heat

    With Th = 600 K, slide «Nguồn lạnh Tc» from 180 to 340 K: efficiency falls as the reservoirs approach each other. Then fix Th and Tc, change «Nhiệt nhận Qh», and confirm η stays the same — only «Wmax = ηQh» and «Qc = Qh − W» scale with Qh. This shows η\eta depends only on the temperatures, not on the size of the cycle.

  3. Read the cycle on the p–V diagram

    Look at the shaded closed loop on the canvas: the «chiều chu trình» (cycle direction) arrow indicates the forward (clockwise) run of an engine, and the enclosed area is proportional to the net work W. Drag the figure to change the viewpoint. Relate the Wmax readout to the area interpretation: W=∮p dVW = \oint p\,dV is positive for a clockwise cycle.

  4. The second-law limit

    Drag Tc close to Th: the efficiency drops toward 0 — no work can be extracted when the reservoirs share a temperature. Conversely set Th = 900 K and Tc = 180 K (the slider limits): η ≈ 80 % is still below 100 %. Predict that η → 1 would require Tc → 0 K, which is unattainable — that is precisely the second-law bound.

Simulation

Experiment history

In 1824 Sadi Carnot published Réflexions sur la puissance motrice du feu, analyzing an ideal reversible cycle of two isotherms and two adiabats. He showed that the efficiency of any heat engine working between two reservoirs is bounded by a limit depending only on the reservoir temperatures, independent of the working substance — remarkable because the heat theory of the time (the caloric picture) was still confused. Rudolf Clausius restated the result in the 1850s on the basis of heat–work equivalence and introduced entropy; William Thomson (Lord Kelvin) proposed the absolute temperature scale in 1848 precisely so the limit could be written η = 1 − Tc/Th. The modern statement of the second law — no engine can beat the Carnot cycle — completed the logic Carnot opened before the first law was even fully formulated.

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