Planning and carrying out an independent investigation

Practical method

Aim

Plan, carry out and evaluate an independent investigation, using the cooling of water by the method of mixtures as the worked example.

Variables

Independent variable: mass of cold water added
Dependent variable: final temperature of the mixture
Control variables: initial temperatures; the same insulated cup; stirring and timing.

Apparatus

• Insulated cup with lid
• Digital thermometer (0.1 °C)
• Balance (0.1 g)
• Kettle
• Cold water
• Stirrer

Method

1. Write a hypothesis using physics: energy lost by the hot water equals energy gained by the cold water.
2. Carry out a pilot run to choose sensible masses and check the timing.
3. Add a measured mass of cold water to a measured mass of hot water, stir and record the highest steady temperature.
4. Repeat for five masses of cold water, repeating each.
5. Compare measured final temperatures with predictions and evaluate.

Sample results

Hot water 100.0 g at 70.0 °C; cold water at 20.0 °C.

Analysis

Measured final temperatures are about 1 °C below the predictions, a consistent (systematic) difference. Energy is lost to the cup and surroundings during mixing. The trend matches the model: more cold water gives a lower final temperature.

Uncertainty

Thermometer ±0.1 °C and balance ±0.1 g give small uncertainties (<0.5%). The main uncertainty is the systematic energy loss, which a lid and fast mixing reduce.

Errors and improvements

Risk assessment

Common mistakes

• Writing a hypothesis without physics reasoning.
• Skipping the pilot run.
• Treating a systematic difference as random scatter.

Worked analysis

Prediction for 100.0 g at 70.0 °C mixed with 50.0 g at 20.0 °C: 100(70 − T) = 50(T − 20), so T = 53.3 °C. Measured 52.1 °C: about 1.2 °C lower because of energy losses.

Common misconception

Agreement within uncertainty is not required for a good investigation; explaining a systematic difference with evidence is part of a strong evaluation.