Theme B — The Particulate Nature of Matter
B.4.8 The Carnot Cycle — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 40 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.4.8 The Carnot Cycle — IB PHYSICS HL notes: Describe the four stages of the Carnot cycle and use the Carnot efficiency 1 − Tc/Th as the maximum efficiency of a heat engine.Aim — Carnot asked what limits the efficiency of a heat engineCarnot cycle — an idealised reversible cycle…
- Isothermal expansion at TH
- Adiabatic expansion
- Isothermal compression at TC
- Adiabatic compression
- p–V diagram
- T–S diagram
Part 1 of 7The ideal engine
1Aim
- Carnot asked what limits the efficiency of a heat engine
2Carnot cycle
- Carnot cycle an idealised reversible cycle between two reservoirs that produces no entropy
3Maximum efficiency
- Maximum efficiency no engine between the same temperatures can be more efficient
- A more efficient engine would move heat from cold to hot without work
4Equality
- Equality all reversible engines between the same reservoirs have the same efficiency
Part 2 of 7The four stages
1Isothermal expansion at TH
- Isothermal expansion at TH the gas absorbs heat QH from the hot reservoir and does work equal to QH
- ΔU = 0 and the pressure falls along an isotherm
2Adiabatic expansion
- Adiabatic expansion the gas is insulated and continues to expand
- Q = 0 and the gas cools from TH to TC
3Isothermal compression at TC
- Isothermal compression at TC heat QC is rejected to the cold reservoir
- Work done on the gas equals QC
4Adiabatic compression
- Adiabatic compression the gas is compressed back to its initial state
- Q = 0 and the gas heats from TC to TH
Part 3 of 7The cycle on diagrams
1p–V diagram
- p–V diagram a clockwise loop of two isotherms and two adiabats
- The enclosed area is the net work per cycle, W = QH − QC
2T–S diagram
- T–S diagram isothermal stages are horizontal lines and adiabatic stages are vertical lines because entropy is constant
3Heat exchange
- Heat exchange it occurs only in the isothermal stages
Part 4 of 7Entropy over the cycle
1Isothermal expansion
- ΔS = QH/TH
2Isothermal compression
- ΔS = −QC/TC
3Adiabatic stages
- ΔS = 0
4Whole cycle
- ΔS = 0 so QH/TH = QC/TC
Part 5 of 7Carnot efficiency
Derivation
- Derivation substitute QC/QH = TC/TH into η = 1 − QC/QH
Equation
- ηC = 1 − TC/TH
- Temperatures must be in kelvin
Dependence
- Dependence efficiency rises with a larger temperature difference
- It is independent of the working substance
Limit
- Limit efficiency equals 1 only if TC = 0 K, which is impossible
Practical design
- TC is set by the surroundings near 300 K so engines run as hot as materials allow
Part 6 of 7Real engines and the Carnot limit
1Upper limit
- Upper limit any real engine between TH and TC is less efficient than the Carnot engine
2Causes
- Causes non-quasi-static changes, friction, heat flow across finite temperature differences and non-ideal gas paths
3Power
- Power a Carnot engine would need infinite time per cycle and give no power
- It is a theoretical benchmark
4Test of a claim
- Test of a claim an efficiency above the Carnot value for the temperatures breaks the second law
5Reverse cycle
- Reverse cycle gives an ideal refrigerator or heat pump
Part 7 of 7More from the specification
1
First Law of Thermodynamics
- For an enclosed thermodynamic system, ΔU = Q - W, where the change in internal energy equals heat added minus work done by the system.
2
Carnot Cycle Processes
- An idealized reversible cycle comprising four successive stages: isothermal expansion, adiabatic expansion, isothermal compression,
- and adiabatic compression.
3
Internal Energy of Ideal Gases
- The internal energy of an ideal gas depends solely on thermodynamic temperature, representing the total microscopic kinetic energy of its particles (ΔU ∝ ΔT).
4
Work Done During Volume Changes
- In an expansion process, gas volume increases and work is done by the system on the surroundings (W = ∫ p dV),
- whereas compression decreases volume.
5
Isolated system
- System with no external interaction.
6
Atmospheric pressure
- Pressure of the air, about 1.01 × 105 Pa at sea level.
7
Volume
- The amount of space an object occupies.
8
Piston
- A moving part in a cylinder that applies or receives pressure.
9
Molecule
- Tiny particle of the fluid, too small to be seen.
10
Internal energy
- Total kinetic and potential energy of the particles in a system
11
Thermal energy
- Energy of random molecular motion, increased by friction.
12
Constant volume
- The container is rigid and sealed.
13
Energy transferred
- W = V Q, in joules.What the symbols mean: E or W = energy transferred (J) · Q = charge (C) · V = potential difference (V) · I = current (A) · t = time (s)
14
Kinetic energy
- K = ½mv2, energy of motion.
Key terms
| Term | Meaning |
|---|---|
| Carnot cycle | A reversible cycle of two isothermal and two adiabatic processes between two reservoirs. |
| Carnot efficiency | η = 1 − TC/TH, the maximum efficiency of any engine between two temperatures. |
| Isothermal stage | A stage at constant temperature in which heat is exchanged with a reservoir. |
| Adiabatic stage | An insulated stage in which temperature changes but no heat is exchanged. |
| Reversible engine | An idealised engine producing no net entropy. |
Avoid these mistakes
1
Using Celsius temperatures in the Carnot efficiency formula — use kelvin.
2
Swapping isothermal and adiabatic stages — heat is exchanged only in the isothermal stages.
3
Calling a Carnot engine a practical design — it is a theoretical limit.
4
Saying Carnot efficiency depends on the working gas — it depends only on TH and TC.
5
Thinking real engines reach Carnot efficiency — only reversible engines do.
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