Thermodynamics
High SchoolHeat, temperature and the gas laws
Temperature measures the average kinetic energy of particles; heat Q is energy transferred due to a temperature difference. Absolute temperature uses kelvin: 0 K = −273.15 °C.
Heating a substance: Q = mcΔT (specific heat capacity c), and during a phase change Q = mL (latent heat, temperature constant).
The ideal gas law links pressure, volume and temperature:
The laws of thermodynamics
First law: energy conservation for heat — ΔU = Q − W (internal energy change = heat added − work done by gas). Second law: heat flows spontaneously from hot to cold; the entropy of an isolated system never decreases. Third law: entropy approaches a constant minimum as T → 0 K.
Entropy and the arrow of time
The second law is the deepest asymmetry in physics. Newton's laws work equally forward and backward in time, yet we never see a shattered cup reassemble or heat flow cold-to-hot unaided. The reason is statistical: there are overwhelmingly more disordered microscopic arrangements than ordered ones, so systems evolve toward higher entropy simply because disorder is vastly more probable. Entropy defines time's direction — the "arrow of time".
This limits engines. No heat engine can be perfectly efficient; some energy must be dumped to a cold reservoir. The maximum possible efficiency (Carnot) depends only on the temperatures:
Worked example — heating and melting ice
How much energy converts 0.20 kg of ice at −10 °C into water at 20 °C? Use cice = 2100, cwater = 4186 J·kg⁻¹·K⁻¹, latent heat of fusion Lf = 3.34×10⁵ J·kg⁻¹.
- Warm ice from −10 to 0 °C:
Q₁ = mcΔT = 0.20×2100×10 = 4 200 J. - Melt the ice at 0 °C:
Q₂ = mLf = 0.20×3.34×10⁵ = 66 800 J. - Warm water from 0 to 20 °C:
Q₃ = mcΔT = 0.20×4186×20 = 16 744 J. - Total:
Q = 4 200 + 66 800 + 16 744 = 87 744 J ≈ 87.7 kJ. - Note the melting step dominates — phase change stores huge energy at constant temperature.
This is why ice keeps a drink cold so effectively: absorbing 334 kJ per kg just to melt, before its meltwater even begins to warm.
A gas at 300 K and 1.0×10⁵ Pa is heated to 600 K at constant volume. What is the new pressure?
At constant V, p/T is constant (Gay-Lussac). p₂ = p₁·T₂/T₁ = 1.0×10⁵ × 600/300 = 2.0×10⁵ Pa. Doubling the absolute temperature doubles the pressure — note you must use kelvin, not Celsius.
Why can't a heat engine be 100% efficient?
The second law: converting all heat to work would decrease the total entropy of the universe, which is forbidden. Some heat must be rejected to a cold reservoir. Carnot efficiency 1 − Tc/Th reaches 100% only if Tc = 0 K, which is unattainable (third law).
Why does blowing on hot soup cool it?
It speeds evaporation. The fastest (most energetic) molecules leave as vapour, carrying away disproportionate kinetic energy and lowering the average — this is evaporative cooling. Blowing also removes the warm, humid layer above the soup, sustaining the evaporation rate.
Two identical blocks, one at 80 °C and one at 20 °C, touch. Describe the final state and entropy.
Heat flows from hot to cold until both reach 50 °C (equal masses and c). Total energy is conserved, but total entropy increases: the cold block gains more entropy (ΔS = Q/T with smaller T) than the hot block loses. Spontaneous equalisation always raises entropy.
How the ideas connect
Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.
The key facts, visualised
Worked problems, step by step
Follow each solution line by line, then try to reproduce it on paper before moving on.
Example 1How much heat raises 0.50 kg of water by 20 C? (c = 4200 J/kg/C)
- Q = m*c*dT
- Q = 0.50 * 4200 * 20
Example 2How much heat melts 0.10 kg of ice at 0 C? (Lf = 3.34e5 J/kg)
- Q = m*Lf
- Q = 0.10 * 3.34e5
Now you try
Work each one out first, then tap to reveal the worked answer.