Calculate the efficiency of a heat engine based on the heat input from a hot reservoir and the heat rejected to a cold reservoir.
Last updated: March 2026 | By Summacalculator
Energy from the hot reservoir (fuel, steam, etc.)
Energy rejected to the cold reservoir (exhaust, cooling water)
Thermal efficiency (η) measures how effectively a heat engine converts heat energy into useful work. It is defined as the ratio of net work output to heat input from the hot reservoir. According to the Second Law of Thermodynamics, no real heat engine can be 100% efficient—some heat must always be rejected to a colder reservoir. This fundamental limitation arises because entropy always increases in isolated systems, making it impossible to convert all input heat into useful work.
The theoretical maximum efficiency for any heat engine operating between two temperature reservoirs is given by the Carnot efficiency, which depends only on the absolute temperatures of the hot and cold reservoirs. Understanding thermal efficiency is crucial for evaluating the performance of power plants, engines, refrigeration systems, and heat pumps. Real-world devices always operate below the Carnot limit due to friction, heat losses, and irreversible processes. This calculator helps you determine the actual efficiency of your heat engine based on measured heat input and output values.
Step 1: Enter the heat input (Q_h) from the hot reservoir in Joules or Watts. This is the total thermal energy supplied to the engine—from fuel combustion, steam in a turbine, or solar radiation in a concentrated solar plant.
Step 2: Enter the heat output (Q_c) rejected to the cold reservoir in Joules or Watts. This is the thermal energy that escapes without producing useful work, typically lost through exhaust gases, cooling systems, or radiators.
Step 3: The calculator automatically computes the thermal efficiency using the formula η = 1 - (Q_c / Q_h). It also displays the useful work output (W = Q_h - Q_c) your engine is producing from the input heat.
An engineer is testing a steam turbine in a power plant. The turbine receives 500 kW of thermal energy from heated steam (hot reservoir at 500°C) and rejects 350 kW of waste heat to cooling water (cold reservoir at 30°C). What is the actual thermal efficiency of this turbine, and how does it compare to the Carnot maximum?
The Second Law of Thermodynamics states that entropy always increases in an isolated system. To convert heat into work, some heat must inevitably be rejected to a colder reservoir. The maximum theoretical efficiency (Carnot) depends on the temperature difference between hot and cold reservoirs.
Carnot efficiency (η_Carnot = 1 - T_c/T_h) is the theoretical maximum any heat engine can achieve between two temperatures. Real engines always perform worse due to friction, turbulence, heat losses, and irreversible processes. It serves as a benchmark for evaluating actual engine performance.
Modern internal combustion engines are typically 20-35% efficient. The rest of the fuel's energy is lost as heat through the exhaust (40-50%), coolant system (20-30%), and friction (5-10%). Diesel engines achieve slightly higher efficiencies (30-45%).
Steam turbines achieve efficiencies of 40-50%, while modern combined-cycle power plants reach 60%+. They have fewer moving parts and operate more continuously. Gas turbines achieve 30-40%. These are all higher than car engines due to larger temperature differentials and better operating conditions.
This calculator automates the computation and immediately shows both the efficiency percentage and the useful work output. It helps you quickly evaluate different engine configurations, compare thermal performance, and understand how changing heat input or output affects overall efficiency.
Increase the hot reservoir temperature (superheating steam, higher combustion temperatures), decrease the cold reservoir temperature (better cooling systems), reduce heat losses (better insulation), and minimize friction and other irreversibilities (precision engineering, advanced materials).
Efficiency tells you what percentage of input heat becomes useful work: W = η × Q_h. A 30% efficient engine with 1000 kW input produces 300 kW of work. Higher efficiency means more work from the same energy input, directly reducing fuel consumption and operating costs.
Calculate the efficiency for each engine using its measured heat input and rejection. The one with the higher efficiency percentage converts more heat to useful work. You can also use Carnot efficiency to see how close each engine approaches its theoretical limit given its temperature extremes.