Changes of State

Aim

• Measure the specific heat capacity of a sample (a metal block, a beaker of water, or both) by heating it electrically and recording the energy supplied alongside the temperature rise

Variables

• Independent variable: time t (s), how long the immersion heater has been running
• Dependent variable: temperature T (°C) of the sample
• Control variables: the same mass of sample, the same supply voltage, the same immersion heater, the same sample container, the same starting room temperature

Apparatus

Method (water variant)

1. Stand an empty 400 ml beaker on the digital balance and press the tare button to zero the reading; pour in about 250 ml of water and write down the new mass m in kg
2. Stand the immersion heater and the thermometer vertically in the water; clamp them so neither touches the bottom of the beaker
3. Connect the circuit: power supply → ammeter (in series) → immersion heater. Wire the voltmeter directly across the heater
4. Note the starting temperature on the thermometer before any current is switched on; this is the baseline for ΔT
5. Switch on the power supply at about 12 V. Start the stopwatch at the same instant
6. Record the voltage V, the current I, and the temperature T every 60 s for 10 minutes. Stir the water gently between readings
7. Switch off the supply. Allow the water to keep warming for a further minute (the heater is still hot, so there's a lag) and record the maximum temperature reached

Method (solid block variant)

• Identical to the water method, except: the immersion heater goes into a hole drilled in the block; thermometer goes into a separate hole. Pack the block with insulating material to cut heat losses, since solids don't stir themselves

Analysis

• The total electrical energy delivered up to time t is:

ΔQ = V × I × t

• Plot a graph of ΔQ (y-axis) against m × ΔT (x-axis), where ΔT is the rise above the starting temperature
• The graph should be a straight line through the origin once the heater itself has warmed up. The gradient of the linear region is the specific heat capacity:

gradient = ΔQ / (m × ΔT) = c

• For pure water you should land near 4200 J/(kg °C); for an aluminium block, near 900 J/(kg °C). A modest discrepancy (typically 5–15 % high) is expected because some energy leaks to the surroundings rather than going into the sample

Sources of error and safety

• Systematic, heat loss to the surroundings. The hot beaker/block warms the room air. Lagging the sample with polystyrene reduces this; using the gradient (which is less affected than a single-point answer) helps too
• Systematic, heater itself absorbing energy. Some of the early electrical energy heats the metal sheath of the immersion heater rather than the sample. Only use the straight-line part of the graph (after the initial dog-leg) when taking the gradient
• Random, temperature gradients across the sample. Stir water samples; insulate solid samples and let them warm slowly so the heat spreads evenly inside
• Safety. Use a low-voltage d.c. supply only, because mains voltage with an immersion heater in water is lethal. The heater becomes very hot; lift it out by the wire, not the metal sheath, and let it cool on a heatproof mat