Specific heat capacity of a solid

Practical method

Aim

Determine the specific heat capacity of aluminium from the gradient of a temperature–time graph.

Variables

Independent variable: time of heating
Dependent variable: temperature
Control variables: heater power; mass of the block; insulation.

Apparatus

• 1.00 kg aluminium block with holes for heater and thermometer
• 12 V heater
• Ammeter and voltmeter (or joulemeter)
• Thermometer with a drop of oil
• Insulation
• Stopwatch

Method

1. Insulate the block, insert the heater and the thermometer (with a drop of oil for thermal contact).
2. Switch on, record V and I, and record the temperature every 120 s for 10 minutes.
3. Plot θ against t. The gradient of the straight section is \(\dfrac{\Delta \theta }{\Delta t}\).
4. c = \(\dfrac{P}{m \times \text{gradient}}\), where P = VI.

Sample results

m = 1.00 kg, V = 12.0 V, I = 4.17 A, P = 50.0 W.

Analysis

The graph is a straight line with gradient 0.0556 °C s⁻¹. c = \(\dfrac{50.0}{1.00 \times 0.0556}\) = 900 J kg⁻¹ K⁻¹. In practice the curve starts slowly (the heater warming up) and flattens at higher temperatures as losses grow; use the straight section.

Uncertainty

Thermometer ±0.5 °C over a 33 °C rise is 1.5%; meters add about 1% each. Heat losses make the measured c too high, a systematic error.

Errors and improvements

Risk assessment

Common mistakes

• Using the first and last temperature instead of the gradient.
• Forgetting P = VI.
• Using total time including the warm-up lag.

Worked analysis

Gradient = \(\dfrac{53.3 - 20.0}{600}\) = 0.0556 °C s⁻¹. c = \(\dfrac{P}{m \times \text{gradient}}\) = \(\dfrac{50.0}{1.00 \times 0.0556}\) = 900 J kg⁻¹ K⁻¹.

Common misconception

Specific heat capacity is per kilogram per kelvin; a temperature change of 1 °C equals a change of 1 K.