Determining specific latent heat

Practical method

Aim

Determine the specific latent heat of vaporisation of water, eliminating heat losses by using two heater powers.

Variables

Independent variable: heater power
Dependent variable: mass of water boiled off in a fixed time
Control variables: time interval; the same insulated container.

Apparatus

• Immersion heater in an insulated beaker of water
• Joulemeter (or ammeter and voltmeter)
• Top-pan balance
• Stopwatch

Method

1. Stand the insulated beaker of water with the heater on the balance and bring the water to the boil.
2. Once it is boiling steadily, record the balance reading and start timing.
3. After 300 s, record the new reading: the mass boiled off.
4. Repeat at a second heater power.
5. Energy balance: Pt = mL + ht, where h is the rate of heat loss. Subtracting the two runs eliminates h: L = \(\dfrac{(P_{2} - P_{1})t}{m_{2} - m_{1}}\).

Sample results

Each run lasts 300 s with the water already boiling.

Analysis

L = \(\dfrac{(100 - 60) \times 300}{11.28 - 5.97}\) × 10⁻³ = \(\dfrac{12000}{5.31 \times 10^{-3}}\) = 2.26 × 10⁶ J kg⁻¹, the accepted value. Using a single run at 100 W gives \(\dfrac{30000}{0.01128}\) = 2.66 × 10⁶ J kg⁻¹, too high because of heat losses (about 15 W).

Uncertainty

The balance reads to ±0.01 g, but the difference m₂ − m₁ = 5.31 g carries the combined uncertainty (about 0.4%). Water splashing or condensing back gives larger errors.

Errors and improvements

Risk assessment

Common mistakes

• Starting timing before the water boils.
• Ignoring heat losses.
• Using grams instead of kilograms.

Worked analysis

Two-power method: L = \(\dfrac{(P_{2} - P_{1})t}{m_{2} - m_{1}}\) = \(\dfrac{40 \times 300}{5.31 \times 10^{-3}}\) = 2.26 × 10⁶ J kg⁻¹.

Common misconception

Specific latent heat is the energy to change state without a change in temperature; during boiling the temperature stays at 100 °C while energy breaks intermolecular bonds.

Variations required by some exam boards

Specific latent heat of fusion of ice: melt ice in a funnel with a heater, using a control funnel without a heater to correct for melting by the surroundings; L = \(\dfrac{Pt}{m_{\text{heated}} - m_{\text{control}}}\).