ZIMSEC A Level · Physics · Form 5, Form 6
Temperature and internal energy
Internal energy is the sum of the random kinetic and potential energies of the molecules. Thermodynamic temperature T (K) = θ (°C) + 273.15; absolute zero is 0 K.
Specific heat capacity and latent heat
Q = mcΔθ; Q = mL (latent heat of fusion or vaporisation – energy breaks intermolecular bonds without changing temperature).
Worked example: Find the energy needed to turn 0.20 kg of ice at 0 °C into water at 20 °C (Lf = 3.34 × 10⁵ J kg⁻¹, c = 4 200 J kg⁻¹ K⁻¹).
Melting: 0.20 × 3.34 × 10⁵ = 66 800 J; heating: 0.20 × 4 200 × 20 = 16 800 J
Total = 83 600 J ≈ 8.4 × 10⁴ J
Ideal gases
- pV = nRT = NkT (R = 8.31 J mol⁻¹ K⁻¹, k = 1.38 × 10⁻²³ J K⁻¹).
- Kinetic theory: pV = ⅓Nm⟨c²⟩; mean kinetic energy of a molecule = (3/2)kT.
Worked example: A gas occupies 0.024 m³ at 100 kPa and 300 K. How many moles are there?
n = pV/RT = (1.0 × 10⁵ × 0.024) ÷ (8.31 × 300) = 0.96 mol
First law of thermodynamics
ΔU = q + W (heat supplied to the system plus work done on the system).
Check yourself
- Convert 27 °C to kelvin.
- A gas at 300 K is heated at constant volume until its pressure doubles. Find the new temperature.
- What happens to the mean kinetic energy of gas molecules if the temperature in kelvin doubles?
Show answers
- 300 K (300.15 K)
- 600 K
- It doubles.
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