Thermodynamics
Thermodynamics is the physics of heat, temperature and energy transfer — why a metal spoon feels colder than a wooden one at the same temperature, why a bicycle pump warms up as you compress it, and why no engine ever built can be 100% efficient.
This module walks you through the whole chain: how we measure temperature, how materials expand when heated, how to track energy with calorimetry, how gases behave under the gas laws, how molecular kinetic theory (分子动理论) explains temperature, pressure and internal energy, and how the First and Second Laws tie it all together into engines, refrigerators and entropy.
Scope: the official syllabus lists three thermodynamics topics: the kinetic theory of gases, the ideal gas equation of state and the first law of thermodynamics. Temperature, specific heat and latent heat (calorimetry), changes of state and thermal expansion are the junior-high and 人教版 background these build on. Heat-transfer rate formulas (conduction, Stefan–Boltzmann, Wien), the Carnot cycle, refrigerator COP and entropy calculations are extension material beyond the syllabus.
Almost every thermodynamics problem is really an energy-bookkeeping problem: work out what energy went in, what came out, and what is left over. Get the sign conventions right and these questions become routine.
What the Exam Tests
The syllabus lists three thermal topics: the kinetic theory of gases, the ideal gas equation of state, and the first law of thermodynamics. This module teaches them in these sections: kinetic theory in Kinetic Theory, Molecular Kinetic Theory: Molecules in Motion and Temperature, Pressure & Internal Energy; the gas equation and its graphs in Ideal Gas Law, Ideal Gas Processes & Their Graphs and PV Diagrams; the first law in First Law of Thermodynamics. The matching practice lessons are Gas Laws, Thermodynamic Laws and Kinetic Theory of Gases.
Questions can ask you to apply pV = nRT or p₁V₁/T₁ = p₂V₂/T₂, read a p–V, p–T or V–T diagram, work out the signs in ΔU = Q + W for a process (W is the work done on the gas, as in Chinese textbooks), or explain pressure and temperature through molecular motion.
In our mock papers Thermodynamics gets 7 of the 48 questions. The CSCA publishes the topics but not how many questions each gets, so this split is our own reading of the syllabus. The Second Law & Entropy and Heat Engines, Refrigerators & Efficiency sections (and the Entropy and Heat Engines practice lessons), and topics such as the Carnot cycle and Wien's law, go beyond the syllabus: they are marked in practice and left out of mocks.
Temperature vs Heat
Scope: the syllabus needs the meaning of temperature (温度是分子热运动平均动能的标志) and the kelvin scale. The heat-transfer rate formulas in this section (conduction rate, Stefan–Boltzmann, Wien) are beyond the CSCA syllabus: read them as background.
Temperature measures the average kinetic energy of the particles in a body. Heat is energy in transit from a hotter body to a cooler one. A bathtub of warm water is at a lower temperature than a spark, but it carries far more thermal energy — that is the difference between the two ideas.
Temperature Scales
T(K) = T(°C) + 273.15, so absolute zero is −273.15 °C = 0 K. In Chinese textbooks the kelvin scale is the 热力学温度 T and the Celsius scale is the 摄氏温度 t, with T = t + 273.15 K. A temperature change is the same on both scales (ΔT = Δt: a rise of 1 K is a rise of 1 °C), so Q = mcΔT and ΔL = αL₀ΔT can use either. Converting from Fahrenheit: T(°C) = (T(°F) − 32) × 5/9. Every gas law, radiation and entropy calculation must use Kelvin — Celsius will give a wrong answer because its zero is not absolute zero.
Zeroth Law & Thermal Equilibrium
If A is in thermal equilibrium with C, and B is also in equilibrium with C, then A and B are in equilibrium with each other. That is what makes a thermometer meaningful. Bodies in thermal equilibrium are at the same temperature, with no net heat flow between them.
Conduction
Energy passes through a material by particle collisions and (in metals) by free electrons. Rate: Q/t = kA ΔT / L, where k is thermal conductivity, A the cross-sectional area and L the thickness. Metals have high k; air, wool and foam have very low k, which is why they make good insulators. Doubling the thickness halves the rate of heat loss.
Convection
Heat carried by the bulk movement of a fluid. Warmed fluid expands, becomes less dense and rises; cooler fluid sinks to replace it, setting up a convection current. Convection needs a fluid, so it cannot happen in a solid or a vacuum.
Radiation
All bodies emit electromagnetic waves, and radiation is the only mechanism that works through a vacuum. Beyond the CSCA syllabus: Stefan–Boltzmann: P = εσA T⁴ with σ = 5.67 × 10⁻⁸ W/(m²·K⁴). Because of the fourth power, doubling the absolute temperature multiplies the radiated power by 16. Wien's displacement law gives the peak wavelength: λmax = b/T with b = 2.90 × 10⁻³ m·K. Matt black surfaces are the best emitters and absorbers; shiny silver surfaces are the worst — which is why a vacuum flask has silvered walls and a vacuum gap to block all three mechanisms at once.
Newton's Law of Cooling
The rate of cooling is proportional to the temperature difference between the body and its surroundings. A hot drink cools quickly at first and then more and more slowly as it approaches room temperature.
Key takeaway: Temperature measures average particle KE; heat is energy in transit. T(K) = T(°C) + 273.15. Three transfer modes: conduction, convection (fluids only) and radiation (works in a vacuum); their rate formulas are background beyond the syllabus.
Key Formulas
- T(K) = T(°C) + 273.15
- T(°C) = (T(°F) − 32) × 5/9
- Q/t = kA ΔT / L (conduction)
- P = εσAT⁴, σ = 5.67 × 10⁻⁸ W/(m²·K⁴)
- λmax = b/T, b = 2.90 × 10⁻³ m·K
Worked Example 1
Example 1: A window pane has k = 0.8 W/(m·K), area 2 m², thickness 5 mm, with 20 °C across it. Find the rate of heat loss.
Step 1: Convert thickness: L = 0.005 m.
Step 2: Q/t = kA ΔT/L = 0.8 × 2 × 20 / 0.005 = 6400 W. Doubling the glass thickness would halve this.
Worked Example 2
Example 2: A sphere of radius 0.1 m at 500 K radiates as a black body (ε = 1). Find the power radiated.
Step 1: A = 4πr² = 4π(0.1)² = 0.1257 m².
Step 2: P = εσAT⁴ = 5.67 × 10⁻⁸ × 0.1257 × 500⁴ ≈ 445 W.
Worked Example 3
Example 3: A body glows at 600 K. Find its peak emission wavelength.
λmax = b/T = 2.90 × 10⁻³ / 600 = 4.8 × 10⁻⁶ m (4.8 μm, in the infrared — which is why it feels hot but does not look bright).
Worked Example 4
Example 4: Convert 68 °F to Celsius and Kelvin.
T(°C) = (68 − 32) × 5/9 = 20 °C, so T(K) = 20 + 273.15 = 293 K.
Exam tip: Convert to Kelvin before any radiation, gas law or entropy calculation — Celsius silently gives a wrong answer.
Exam tip: Radiated power goes as T⁴, so a factor-of-2 temperature rise is a factor-of-16 power rise. Radiation laws are beyond the CSCA syllabus: useful background, but left out of our mocks.
Exam tip: Thermos flask questions want all three mechanisms: vacuum stops conduction and convection, silvering stops radiation.
Common mistake: Treating heat and temperature as the same thing: temperature is average particle energy; heat is the energy that flows because of a temperature difference.
Common mistake: Leaving thickness in millimetres: L must be in metres in Q/t = kAΔT/L, or the answer is out by a factor of 1000.
Common mistake: Assuming convection happens in solids: convection needs a fluid that can flow, so a solid metal bar transfers heat by conduction only.
Try This Yourself
A brick wall is 0.2 m thick with k = 0.6 W/(m·K) and area 10 m². Inside is 20 °C, outside is 0 °C. Find the rate of heat loss.
Module Summary
You have finished Thermodynamics. You can now convert between temperature scales, predict thermal expansion, solve calorimetry and phase-change problems, explain temperature, gas pressure and internal energy through molecular motion (Brownian motion, diffusion, intermolecular forces, Ek = (3/2)kT), apply the gas laws and the ideal gas equation, read p–V, p–T and V–T graphs, use the First Law across all four standard processes, read work off a PV diagram, calculate entropy changes, and judge whether an engine or refrigerator is physically possible.
For the exam, the syllabus core is the kinetic theory of gases, the ideal gas equation and the first law ΔU = Q + W (W = work done on the gas), built on the groundwork of temperature, thermal expansion, calorimetry and changes of state; entropy and heat engines go beyond the syllabus. The one habit that carries it all: identify the process, convert to Kelvin and SI units, and get the sign of W right.
Open and read all sections to complete this module