A heat engine is a cyclic device that absorbs heat from a hot reservoir, converts part of it into mechanical work, and rejects the remaining heat to a cold reservoir.
Learning Outcomes
A heat engine converts heat energy into mechanical work.
It requires a hot reservoir, a cold reservoir and a working substance.
The working substance operates cyclically and returns to its initial state.
It absorbs Q₁ from the hot reservoir and rejects Q₂ to the cold reservoir.
Net work per cycle is W = Q₁ − Q₂.
Efficiency is η = WQ₁ = 1 − Q₂Q₁ and is always less than 100% for a real heat engine.
Intermediate Level
Definition and Energy Flow
A heat engine repeatedly converts part of the heat that flows from a high-temperature source to a low-temperature sink into mechanical work. Petrol and steam engines are examples.
Key equation
Q1=W+Q2
Key equation
W=Q1-Q2
Three Essential Parts
Part
Role
Hot reservoir (source)
Maintained at higher temperature T₁ and supplies Q₁.
Working substance
Usually a gas or vapor that receives heat and performs mechanical work.
Cold reservoir (sink)
Maintained at lower temperature T₂ and receives rejected heat Q₂.
Thermal Efficiency
Efficiency is the fraction of input heat converted into net work. Some heat must be rejected, so a real engine cannot convert all Q₁ into work.
Key equation
η=WQ1
Key equation
η=1-Q2Q1
Key equation
η(\%)=WQ1×100
Engine Energy Balance
A heat engine absorbs 1200 J from its hot reservoir and rejects 750 J to its cold reservoir each cycle. Find work and efficiency.
1
Working
W = Q₁ − Q₂ = 1200 J − 750 J
2
Step 2
W = 450 J
3
Step 3
η = WQ₁ = 4501200 = 0.375
Final answer:W = 450 J and η = 37.5%
Why Cyclic Operation Matters
After one complete cycle the working substance returns to its starting state, so its net internal-energy change is zero. The net heat received over the cycle therefore equals the net work produced.
Common Mistakes
Do not treat Q₂ as useful work; it is heat rejected.
Use W = Q₁ − Q₂, not Q₁ + Q₂.
Efficiency uses input heat Q₁ in the denominator.
A cold reservoir is essential for continuous cyclic operation.
Short-Question Preparation
Q. Define a heat engine.
A. A cyclic device that converts part of heat absorbed from a hot reservoir into mechanical work and rejects the rest to a cold reservoir.
Q. Name its three essential parts.
A. Hot reservoir, cold reservoir and working substance.
Q. Write the energy equation.
A.W = Q₁ − Q₂.
Q. Define thermal efficiency.
A.η = WQ₁ = 1 − Q₂Q₁.
Sticky Notes
A heat engine converts heat energy into mechanical work.
It requires a hot reservoir, a cold reservoir and a working substance.
The working substance operates cyclically and returns to its initial state.
It absorbs Q₁ from the hot reservoir and rejects Q₂ to the cold reservoir.
Net work per cycle is W = Q₁ − Q₂.
Efficiency is η = WQ₁ = 1 − Q₂Q₁ and is always less than 100% for a real heat engine.
60-Second Revision
A heat engine absorbs Q₁ at T₁, produces W, and rejects Q₂ at T₂. Energy conservation gives W = Q₁ − Q₂. Its three parts are the source, working substance and sink; η = WQ₁.
Summary
A heat engine is a cyclic device that absorbs heat from a hot reservoir, converts part of it into mechanical work, and rejects the remaining heat to a cold reservoir.
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Exam preparation
Exam Focus
Important points
A heat engine converts heat energy into mechanical work.
It requires a hot reservoir, a cold reservoir and a working substance.
The working substance operates cyclically and returns to its initial state.
It absorbs Q₁ from the hot reservoir and rejects Q₂ to the cold reservoir.
Net work per cycle is W = Q₁ − Q₂.
Efficiency is η = WQ₁ = 1 − Q₂Q₁ and is always less than 100% for a real heat engine.
Common mistakes
Do not treat Q₂ as useful work; it is heat rejected.
Use W = Q₁ − Q₂, not Q₁ + Q₂.
Efficiency uses input heat Q₁ in the denominator.
A cold reservoir is essential for continuous cyclic operation.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Heat Engine
Sticky Notes · Quick Revision
1.
Key Point 1
A heat engine converts heat energy into mechanical work.
2.
Key Point 2
It requires a hot reservoir, a cold reservoir and a working substance.
3.
Key Point 3
The working substance operates cyclically and returns to its initial state.
4.
Key Point 4
It absorbs Q₁ from the hot reservoir and rejects Q₂ to the cold reservoir.
