Internal Energy and Specific Latent Heat
Internal Energy and Specific Latent Heat
When you heat a substance, its temperature does not always rise. During a change of state, energy goes into breaking bonds between particles rather than increasing their speed. This is where latent heat comes in.
Internal Energy
The internal energy of a system is the total kinetic energy and potential energy of all the particles in the system.
- Kinetic energy of particles depends on their speed — related to temperature
- Potential energy of particles depends on the spacing and bonds between them — related to state
When you heat a substance:
- If the temperature rises, the kinetic energy of the particles increases (they move faster)
- If a change of state occurs, the potential energy of the particles increases (bonds break) but the temperature stays constant
Heating and Cooling Curves
A heating curve shows how the temperature of a substance changes over time as it is heated at a constant rate.
- Sloping sections = temperature rising (kinetic energy increasing, substance staying in one state)
- Flat sections = change of state occurring (potential energy increasing, temperature constant)
For water being heated from ice:
1. Solid ice warms up (slope)
2. Ice melts at 0 degC (flat — melting point)
3. Liquid water warms up (slope)
4. Water boils at 100 degC (flat — boiling point)
5. Steam warms up (slope)
A cooling curve shows the reverse — flat sections appear at the boiling point (condensing) and melting point (freezing).
Specific Latent Heat
Specific latent heat is the energy required to change the state of 1 kg of a substance with no change in temperature.
energy for a change of state = mass x specific latent heat
E = m x L
Where:
- E = energy (joules, J)
- m = mass (kilograms, kg)
- L = specific latent heat (J/kg)
There are two types:
Specific latent heat of fusion (L_f) — the energy needed to change 1 kg of solid to liquid (or liquid to solid) at the melting point.
Specific latent heat of vaporisation (L_v) — the energy needed to change 1 kg of liquid to gas (or gas to liquid) at the boiling point.
For water:
- L_f (fusion) = 334,000 J/kg (334 kJ/kg)
- L_v (vaporisation) = 2,260,000 J/kg (2,260 kJ/kg)
The latent heat of vaporisation is much larger than the latent heat of fusion because during boiling, particles must completely overcome all the attractive forces between them, which requires far more energy than merely loosening them (melting).
Example: How much energy is needed to melt 0.5 kg of ice at 0 degC?
E = m x L_f = 0.5 x 334,000 = 167,000 J (167 kJ)
This energy melts the ice but does not raise its temperature. To then heat the water to, say, 100 degC, you would need to add further energy using E = m x c x delta-theta.
Required Practical: Investigating Specific Latent Heat
Aim: To determine the specific latent heat of fusion of ice (or vaporisation of water).
Method (for fusion of ice):
1. Set up an insulated beaker with a heater and thermometer
2. Place crushed ice in the beaker
3. Allow the ice to start melting naturally — measure the mass of water that melts WITHOUT the heater over a set time (this is the control — accounts for heat from the room)
4. Repeat with the heater on for the same time — measure the extra mass of water that melts
5. Use a joulemeter (or E = P x t) to measure the energy supplied by the heater
6. Calculate: L = E / m (using the extra mass melted by the heater)
Sources of error:
- Energy absorbed from the surroundings (the control helps correct for this)
- Some energy heats the water rather than melting ice — the answer tends to be higher than the accepted value
Exam Tips
- "Latent" means "hidden" — the energy is hidden because the temperature does not change
- On heating curves, always label both the flat sections with the correct change of state
- When calculating total energy to heat AND change state, you may need to use BOTH equations (E = mcDT and E = mL) and add the results