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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

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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

TermMeaning
Heat engineA 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 reservoirThe source at temperature TH from which the engine takes heat.
Cold reservoirThe sink at temperature TC to which waste heat is rejected.
Closed cycleA 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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