Carnot efficiency: use absolute temperatures, not Celsius ratios
Calculate an ideal heat-engine limit and compare it with efficiency from measured heat and work.
Method
Carnot efficiency is an ideal upper bound for a heat engine operating between hot and cold reservoirs. It is one minus the cold absolute temperature divided by the hot absolute temperature. Both temperatures must be positive in kelvins, with the hot reservoir warmer than the cold one. Converting only the temperature difference is insufficient: the formula uses a ratio of absolute readings. This bound describes an ideal reversible engine, not the expected performance of a real installation.
Worked example
Convert each Celsius reading in the example before forming the ratio. Using the original Celsius values produces a plausible-looking but incorrect percentage. The separate heat-and-work example computes an actual efficiency below the ideal bound. Use Carnot efficiency for reservoir temperatures and Heat engine efficiency for heat supplied and rejected. Compare values only when their system boundary and energy accounting match.
Th = 227 °C + 273.15 = 500.15 K
Tc = 27 °C + 273.15 = 300.15 K
ηmax = (1 − 300.15 / 500.15) × 100 ≈ 39.988%
(1 − 27 / 227) × 100 ≈ 88.106%
Qh = 1000 J; Qc = 650 J; W = 350 J
η = 350 / 1000 × 100 = 35%
Checks and limits
Raising the hot reservoir temperature or lowering the cold reservoir temperature increases this ideal limit. Practical material limits, heat transfer and irreversible losses constrain real operation. Equal reservoir temperatures give no Carnot work potential, while a colder designated hot reservoir is an invalid heat-engine arrangement. Do not infer fuel consumption, electric output or financial savings from the bound alone. A calculated real efficiency above the applicable bound calls for checking measurements, units and system boundaries rather than claiming a more efficient engine.
Related calculators
Source: OpenStax — Carnot heat engines