1. What Is Efficiency?
Efficiency of a heat engine tells us how well the engine converts heat into useful work. A perfectly efficient engine would convert all input heat into work, but real engines always waste some heat.
Efficiency is always less than 100%.
2. Efficiency Formula for Heat Engines
The basic definition of efficiency is the ratio of useful work output to heat input:
\( \eta = \dfrac{W}{Q_h} \)
Using the First Law (\( Q_h = W + Q_c \)), efficiency can also be written as:
\( \eta = 1 - \dfrac{Q_c}{Q_h} \)
2.1. Meaning of Terms
- \( Q_h \): heat absorbed from the hot source
- \( W \): work done by the engine
- \( Q_c \): heat rejected to the cold sink
2.2. Why Efficiency Is Always < 1
Some heat must always be rejected due to the Second Law. This makes \( Q_c \) nonzero, so efficiency is always less than one.
3. Carnot Efficiency (Maximum Possible Efficiency)
The highest efficiency a heat engine can theoretically achieve is given by the Carnot efficiency. It depends only on the temperatures of the hot and cold reservoirs.
3.1. Carnot Efficiency Formula
\( \eta_{max} = 1 - \dfrac{T_c}{T_h} \)
Where \( T_h \) and \( T_c \) are in Kelvin.
3.2. Meaning of Carnot Efficiency
The larger the temperature difference, the higher the efficiency. If the cold reservoir is very cold, efficiency improves.
4. Factors Affecting Efficiency of Real Engines
Real engines have lower efficiency than the Carnot limit due to several unavoidable factors.
4.1. 1. Friction and Mechanical Losses
Moving parts lose energy due to friction, reducing useful work output.
4.2. 2. Heat Loss to Surroundings
Engines release heat to the environment through conduction, convection, and radiation.
4.3. 3. Imperfect Combustion
In combustion engines, not all fuel burns completely, reducing available heat.
4.4. 4. Finite Temperature Differences
Heat transfer requires a temperature difference, making perfect reversibility impossible.
4.5. 5. Real-World Material Limits
Materials cannot withstand extremely high temperatures, so \( T_h \) cannot be increased indefinitely.
5. Improving Engine Efficiency
Engineers use various methods to improve efficiency, though it can never reach 100%.
5.1. Methods
- Increasing compression ratio (in internal combustion engines)
- Using better lubricants to reduce friction
- Recovering waste heat using turbochargers or heat exchangers
- Optimizing fuel-air mixture
- Using higher temperature sources where possible
6. Examples of Engine Efficiencies
- Petrol engine: around 25–30%
- Diesel engine: about 30–40%
- Steam turbine: 35–45%
- Modern combined-cycle power plants: up to 60%
None of these reach Carnot efficiency, but they get closer with better designs.