Thermal Efficiency Calculator
Calculate thermal efficiency from work output, heat input, rejected heat, and Carnot reservoir temperatures.
Understanding Thermal Efficiency
Thermal efficiency measures how much of the heat supplied to an engine becomes useful work. Power plants, car engines, and industrial boilers never convert 100% of input heat into work because some energy must be rejected to a colder reservoir. Efficiency is always between 0 and 1, or 0% and 100%.
Efficiency Formulas
From energy accounting:
$$\eta = \frac{W_{out}}{Q_{in}} = 1 - \frac{Q_{out}}{Q_{in}}$$The Carnot limit gives the maximum possible efficiency for a heat engine operating between a hot reservoir at $T_h$ and a cold reservoir at $T_c$ (both in kelvin):
$$\eta_{Carnot} = 1 - \frac{T_c}{T_h}$$Real engines fall below this limit because of friction, incomplete combustion, and finite heat-transfer rates. See also our Carnot Efficiency Calculator and Thermal Energy Calculator.
Frequently Asked Questions
Can thermal efficiency exceed 100%?
No. Efficiency above 100% would violate conservation of energy. Useful work output cannot be greater than heat input unless additional energy sources are included, which is outside the standard heat-engine definition.
Why must temperatures be in kelvin for Carnot efficiency?
Carnot's theorem uses absolute temperature scales. Celsius differences work for simple $\Delta T$ problems, but the ratio $T_c/T_h$ requires kelvin because 0 K is true absolute zero.
What is a typical power plant efficiency?
Modern combined-cycle gas plants may reach roughly 60% thermal efficiency. Coal plants are often near 35-40%. Automobile engines are typically below 30% because of wide operating conditions and mechanical losses.
How is rejected heat calculated?
By energy balance, $Q_{out} = Q_{in} - W_{out}$. The calculator uses this relationship whenever you supply heat input and either work output or rejected heat.
What is the difference between thermal and Carnot efficiency?
Thermal efficiency is the actual ratio of work to heat input for a real device. Carnot efficiency is the theoretical upper bound for any reversible engine between the same two reservoir temperatures.
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