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Thermodynamics Formula

What is Carnot Efficiency?

The maximum possible efficiency of a heat engine operating between two temperature reservoirs.

Formula: \eta = 1 - \frac{T_c}{T_h}

Plain-English Meaning

No heat engine can be 100% efficient — some heat must always be wasted. The Carnot cycle sets the absolute upper limit on efficiency. The bigger the difference between the hot (T_h) and cold (T_c) reservoirs, the more efficient you can be.

Write the system boundary first. Many thermodynamics mistakes disappear once you know what counts as heat, work, and internal-energy change.

Deeper Explanation

η = 1 − T_c/T_h (temperatures in Kelvin). Carnot cycle: two isothermal + two adiabatic steps. For a refrigerator: COP = T_c/(T_h − T_c). Any real engine has η < η_Carnot because real processes are irreversible.

Worked Example

Problem: A steam engine operates between 600 K steam and 300 K exhaust. What is the maximum efficiency?

  • η = 1 − T_c/T_h
  • η = 1 − 300/600
  • η = 1 − 0.5 = 0.5

Result: Maximum efficiency = 50%

At A Glance

Category: Thermodynamics

Levels covered: High School, College, Masters, PhD

Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.