Theme B — The Particulate Nature of Matter
B.4.7 Heat Engines — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 39 of 53 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
B.4.7 Heat Engines — IB PHYSICS HL notes: Describe how a cyclic heat engine converts heat into work, and calculate net work, efficiency and energy flows from p–V loops.Definition — a device that converts thermal energy into mechanical work in a continuous closed cycleClosed cycle…
- Simple engine
- Over one cycle
- Second law
- Power form
- Heat flows
- Power stations
Part 1 of 8What a heat engine is
1Definition
- Definition a device that converts thermal energy into mechanical work in a continuous closed cycle
2Closed cycle
- Closed cycle the working substance returns to its initial state at the end of each cycle
3Simple engine
- Simple engine a gas in a cylinder with a piston
4Examples
- Examples petrol and diesel engines, steam turbines and jet engines
Part 2 of 8Steps of a cyclic engine
1
Heat QH is extracted from a hot reservoir at temperature TH.
2
The gas uses some of it to do work as it expands and pushes the piston out.
3
The gas cools at constant volume and excess heat QC is released to a cold reservoir at TC.
4
The piston compresses the gas back to its original state and the cycle repeats.
Part 3 of 8Energy balance
1Over one cycle
- ΔU = 0 so the first law gives Qnet = W
2Net work
- Wout = QH − QC
3QH
- QH heat from the hot reservoir to the engine in J
4QC
- QC heat from the engine to the cold reservoir in J
5Second law
- QC cannot be zero, so not all heat becomes work
Part 4 of 8Efficiency
Definition
- Definition efficiency = useful work output ÷ total energy input
Equation
- η = Wout/QH = (QH − QC)/QH = 1 − QC/QH
Value
- η has no unit and is always less than 1
- It is often quoted as a percentage
Power form
- η = Pout/Pin when energy flows are given as rates
Limit
- Limit efficiency does not tell how fast work is produced
Part 5 of 8Heat engines on p–V diagrams
1Loop
- Loop a cycle is a closed loop and the enclosed area is the net work per cycle
2Direction
- Direction a clockwise loop gives positive work (an engine)
- An anticlockwise loop means work is done on the gas, as in a refrigerator
3Analysis
- Analysis identify the process type of each segment, find Q, W and ΔU for each, and check ΔU sums to zero
4Heat flows
- QH is the sum of positive Q values and QC is the size of the sum of negative Q values
5Check
- W = QH − QC must equal the loop area
Part 6 of 8Real engines
Power stations
- Power stations about 35% to 40% efficiency because steam temperatures are limited by materials
- Combined-cycle plants reach about 60%
Car engines
- 25% to 30% because of friction, incomplete combustion and hot exhaust
Waste heat
- Waste heat energy spread out at low temperature that can no longer do work
Upper limit
- Upper limit the Carnot efficiency for the same temperatures
Part 7 of 8Reverse cycles
1Refrigerator and heat pump
- Refrigerator and heat pump work W is done on the gas, heat Qc is taken from a cold region and Qh = Qc + W is delivered to a hot region
2Second law
- Second law this obeys the Clausius form because work is supplied
Part 8 of 8More from the specification
1
Heat engine
- Heat engine takes thermal energy from a hot reservoir, does work and rejects heat to a cold reservoir, with efficiency limited by temperatures
2
Entropy
- Entropy a measure of disorder, and the second law of thermodynamics states total entropy of a system and surroundings never decreases
3
Adiabatic process
- Adiabatic process no heat is exchanged with the surroundings, so change in internal energy equals work done
4
Ideal gas cycle
- Ideal gas cycle pV diagrams show net work as enclosed area, and Carnot efficiency is one minus cold over hot temperature
5
Isolated system
- System with no external interaction.
6
Atmospheric pressure
- Pressure of the air, about 1.01 × 105 Pa at sea level.
7
Entropy
- A measure of the number of possible arrangements of particles and energy, S = kB ln Ω.
8
Adiabatic
- With no thermal energy transfer
9
Isothermal
- At constant temperature
10
Expansion
- Increase in size on heating as particles move further apart.
11
Molecule
- Tiny particle of the fluid, too small to be seen.
12
Surroundings
- Everything outside the system.
13
Internal energy
- Total kinetic and potential energy of the particles in a system
14
Temperature change
- Δθ, final temperature minus initial temperature.
Key terms
| Term | Meaning |
|---|---|
| Heat engine | A device that converts heat from a hot reservoir partly into work, operating in a cycle. |
| Efficiency (η) | W/QH, the fraction of input heat converted into useful work. |
| Hot reservoir | The source at temperature TH from which the engine takes heat. |
| Cold reservoir | The sink at temperature TC to which waste heat is rejected. |
| Closed cycle | A sequence of processes returning a system to its initial state. |
Avoid these mistakes
1
Using QH − QC with a negative QC — QC is the magnitude of heat rejected.
2
Calculating efficiency as W/QC — it is W/QH.
3
Saying an engine is 100% efficient if friction is removed — heat must still be rejected.
4
Forgetting ΔU = 0 over a complete cycle.
5
Reading a clockwise loop as work done on the gas — it is work done by the gas.
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