Internal Energy and Energy Transfers (P3.2)

Internal energy

Internal energy is the total kinetic and potential energy of all the particles in a substance.

• Kinetic energy: energy due to particle motion (vibration, translation, rotation).
• Potential energy: energy due to the positions of particles (intermolecular forces).

When a substance is heated:

• If the substance changes temperature: kinetic energy of particles increases.
• If the substance changes state: potential energy increases (intermolecular bonds broken); kinetic energy stays constant → temperature stays constant.

Specific heat capacity (recap)

ΔE = mcΔθ

m = mass (kg), c = SHC (J/kg°C), Δθ = temperature change.

Specific latent heat

Latent heat is the energy absorbed or released during a change of state at constant temperature.

E = mL

E = energy (J), m = mass (kg), L = specific latent heat (J/kg).

Specific latent heat of fusion (Lf): energy to change 1 kg from solid to liquid (or vice versa) at constant temperature.
Specific latent heat of vaporisation (Lv): energy to change 1 kg from liquid to gas (or vice versa).

Values for water:
Lf = 334,000 J/kg (334 kJ/kg) — melting/freezing
Lv = 2,260,000 J/kg (2.26 MJ/kg) — boiling/condensing

Note: Lv >> Lf — much more energy needed to fully separate particles in vaporisation than in melting.

Worked example: How much energy is needed to melt 2 kg of ice at 0°C?
E = mL = 2 × 334,000 = 668,000 J = 668 kJ

Required practical: specific heat capacity

Set up: immersion heater in a known mass of water/metal block; measure power (P = IV), time, and temperature change. Calculate c = E/(mΔθ).

Temperature-time heating curve

The heating curve for water (starting as ice):

1. Ice heats up (slope) — SHC of ice
2. Flat region at 0°C — melting (latent heat of fusion)
3. Water heats up (slope) — SHC of water
4. Flat region at 100°C — boiling (latent heat of vaporisation)
5. Steam heats up (slope)

Common exam errors

1. Saying "latent heat is stored at a constant temperature" — it is used to break bonds; temperature remains constant because KE doesn't change.
2. Confusing Lf and Lv — Lv is about 7× larger because all intermolecular bonds must be broken to vaporise.
3. Forgetting units — L is in J/kg, so mass must be in kg.