Carnot Efficiency Calculator

What Is Carnot Efficiency?

The Carnot cycle defines the maximum efficiency any heat engine can achieve when operating between two temperature reservoirs. No real engine reaches this limit because isothermal steps are slow and losses occur, but Carnot efficiency sets the theoretical ceiling.

Carnot Efficiency Formula

$$\eta = 1 - \frac{T_c}{T_h} = \frac{T_h - T_c}{T_h}$$

Temperatures must be in Kelvin. Example: $T_h = 400$ K and $T_c = 300$ K give $\eta = 1 - 300/400 = 25\%$.

Work Output and Refrigerator COP

Maximum work from heat input $Q_h$:

$$W_{max} = \eta \cdot Q_h$$

Coefficient of performance for a reversible refrigerator:

$$COP = \frac{T_c}{T_h - T_c}$$

A refrigerator moves heat from cold to hot by doing work. Higher COP means more cooling per unit of work input.

Frequently Asked Questions

Why must temperatures be in Kelvin?

Carnot efficiency uses absolute temperature ratios. Celsius differences only match Kelvin differences, but the ratio $T_c/T_h$ requires Kelvin values.

Can a real engine match Carnot efficiency?

No. Real engines have friction, finite-rate heat transfer, and non-ideal working fluids. Carnot efficiency is an upper bound, not an achievable target.

What is refrigerator COP?

COP measures cooling delivered per unit of work input. For a Carnot refrigerator, $COP = T_c/(T_h - T_c)$. Higher is better for cooling performance.

How do I find maximum work?

Multiply Carnot efficiency by the heat absorbed from the hot reservoir: $W_{max} = \eta Q_h$. Enter $Q_h$ in joules.

What happens if hot and cold temperatures are equal?

Efficiency drops to zero and COP becomes undefined. A temperature difference is required to produce work or transfer heat against the gradient.

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What Is Carnot Efficiency?

Carnot Efficiency Formula

Work Output and Refrigerator COP

Frequently Asked Questions

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