Differences and Similarities Between PV Curves for a Carnot Engine and a Real Engine
Dec 2
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BTEC Applied Science – Unit 5: Principles and Applications of Physics II
Engines convert heat energy into mechanical work — but not all engines are equally efficient. The Carnot cycle represents an ideal, perfectly efficient heat engine, while real engines always lose some energy as heat or friction. In Unit 5, you compare PV (pressure–volume) curves to understand this difference.
What Is a PV Curve?
A PV diagram shows how the pressure and volume of a gas change during one full cycle of an engine. The area inside the loop represents the work done by the gas.
The Carnot Cycle (Ideal Engine)
A Carnot engine is a theoretical, idealised heat engine that represents the most efficient possible way to convert heat into work. It's not real, but it's how we would like an engine to be.
The Carnot engine containing a gas fuel, operates through four reversible stages. In each stage, the graph represents what it happening to the gas:
1 to 2 - Isothermal expansion – gas expands at constant temperature (absorbs heat from hot -reservoir).
2 to 3 - Adiabatic expansion – gas continues to expand without heat exchange (temperature falls).
3 to 4 - Isothermal compression – gas is compressed at low temperature (releases heat).
4 to 1 - Adiabatic compression – gas returns to starting state.
Efficiency: The Carnot engine is a theoretical ideal, representing the maximum possible efficiency for any heat engine
The Real Engine (Otto Cycle)
Conversely, a real engine describes one where most petrol car engines use a four-stroke process to turn fuel into motion, while accounting for real-world inefficiencies and mechanical losses.
In terms of the gas fuel, real engines (like petrol or diesel engines) show:
Irreversible processes – friction, turbulence, incomplete combustion.
Heat loss – not all heat converted to work.
Non-ideal compression and expansion – curves less sharp and asymmetrical.
In each stage, the graph represents what it happening to the gas:
1 to 2 - Fuel intake: The piston moves downward (volume increases), drawing in a fresh air-fuel mixture. The pressure during this stage is relatively constant, due to the vacuum effect created by the piston movement.
2 to 3 - Compression Stroke: The piston moves up, compressing the air-fuel mixture causing the volume to decrease, and the pressure and temperature to increase.
3 to 4 - Combustion (or Power) Stroke: At the top of the compression stroke, a spark ignites the fuel. This rapid combustion causes an instantaneous increase in pressure and temperature while the piston is briefly stationary.
4 to 5 - Expansion. After combustion, the piston begins to move downward. This allows the hot, high-pressure gases to expand. As the volume increases, the pressure and temperature decrease (following an adiabatic expansion). This is where useful work is done on the piston, driving the crankshaft.
5 to 6 - Exhaust Stroke: The exhaust valve opens, and the piston moves up, pushing the spent (burned) gases out of the cylinder. The pressure drops to atmospheric levels, and the volume returns to its starting minimum
Comparison Summary
Feature | Carnot Engine | Real Engine |
Process | Ideal and reversible | Real and irreversible |
Heat transfer | No losses | Heat lost to surroundings |
PV curve | Smooth, rectangular | Smaller, distorted loop |
Efficiency | Maximum possible | Always lower |
Example | Theoretical model | Petrol, diesel, steam turbines |
Exam Tip
“The Carnot engine represents the maximum efficiency possible between two temperatures. Real engines are less efficient because of friction, turbulence, and heat loss — shown by a smaller PV loop.”
Exam practice question
Explain why the Carnot engine is an ideal engine (4 marks)
A Carnot cycle engine contains a fixed mass of gas. The piston head in the engine cylinder moves downwards, decreasing the volume in the cylinder. Explain what happens to the internal energy of the gas. Your answer should refer to:
-the motion of the gas molecules
-the gas temperature. (4 marks)
Model answer
1.Explain why the Carnot engine is an ideal engine (4 marks)
A Carnot engine is ideal because it operates using only reversible processes, meaning there are no energy losses from friction or heat transfer inefficiencies. It has no wasteful energy losses, so all heat transfers occur so slowly that the system stays in thermal and mechanical equilibrium at every moment.
As a result, it achieves the maximum possible efficiency allowed by the laws of thermodynamics for given hot and cold reservoir temperatures. No real engine can exceed this efficiency, making the Carnot engine a perfect theoretical benchmark.
2. Internal energy changes when the volume decreases (4 marks)
When the piston moves downwards, the volume decreases, compressing the gas. The gas molecules are forced closer together and collide more frequently and with greater speed.
This increases the average kinetic energy of the molecules. Because temperature is a measure of the average kinetic energy, the temperature of the gas rises, so the internal energy increases.
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