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AQA GCSE · Question 10.5 · Energy changes
The student repeated the experiment for 8.0 g of ammonium nitrate three more times. The student recorded the mean lowest temperature as 16.5 ± 0.3 °C. Explain why the student included ± 0.3 °C after the mean lowest temperature.
<div style="font-family: Arial, sans-serif; max-width: 700px;">
<h3 style="text-align: center;">Table 7</h3>
<table style="width: 100%; border-collapse: collapse; text-align: center; border: 1px solid black;">
<thead>
<tr>
<th style="border: 1px solid black; padding: 10px; width: 30%;"></th>
<th style="border: 1px solid black; padding: 10px;">Trial 1</th>
<th style="border: 1px solid black; padding: 10px;">Trial 2</th>
<th style="border: 1px solid black; padding: 10px;">Trial 3</th>
<th style="border: 1px solid black; padding: 10px;">Trial 4</th>
<th style="border: 1px solid black; padding: 10px; font-weight: bold;">Mean</th>
</tr>
</thead>
<tbody>
<tr>
<td style="border: 1px solid black; padding: 10px; font-weight: bold; text-align: left;">Lowest temperature of solution in °C</td>
<td style="border: 1px solid black; padding: 10px;">16.2</td>
<td style="border: 1px solid black; padding: 10px;">16.6</td>
<td style="border: 1px solid black; padding: 10px;">16.8</td>
<td style="border: 1px solid black; padding: 10px;">16.4</td>
<td style="border: 1px solid black; padding: 10px; font-weight: bold;">16.5</td>
</tr>
</tbody>
</table>
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The student repeated the experiment for 8.0 g of ammonium nitrate three more times. The student recorded the mean lowest temperature as 16.5 ± 0.3 °C. Explain why the student included ± 0.3 °C after the mean lowest temperature.
<div style="font-family: Arial, sans-serif; max-width: 700px;"> <h3 style="text-align: center;">Table 7</h3> <table style="width: 100%; border-collapse: collapse; text-align: center; border: 1px solid black;"> <thead> <tr> <th style="border: 1px solid black; padding: 10px; width: 30%;"></th> <th style="border: 1px solid black; padding: 10px;">Trial 1</th> <th style="border: 1px solid black; padding: 10px;">Trial 2</th> <th style="border: 1px solid black; padding: 10px;">Trial 3</th> <th style="border: 1px solid black; padding: 10px;">Trial 4</th> <th style="border: 1px solid black; padding: 10px; font-weight: bold;">Mean</th> </tr> </thead> <tbody> <tr> <td style="border: 1px solid black; padding: 10px; font-weight: bold; text-align: left;">Lowest temperature of solution in °C</td> <td style="border: 1px solid black; padding: 10px;">16.2</td> <td style="border: 1px solid black; padding: 10px;">16.6</td> <td style="border: 1px solid black; padding: 10px;">16.8</td> <td style="border: 1px solid black; padding: 10px;">16.4</td> <td style="border: 1px solid black; padding: 10px; font-weight: bold;">16.5</td> </tr> </tbody> </table> </div>How to approach this question
1. The "±" symbol indicates the uncertainty in a measurement.\n2. Uncertainty is calculated from the range of the repeat readings.\n3. First, find the range of the results in Table 7 (highest value - lowest value).\n4. The uncertainty is then calculated as half of the range.\n5. Explain that the ± 0.3 °C value represents this calculated uncertainty.
Full Answer
It shows the uncertainty of the measurement. The range of the results was from 16.2 °C to 16.8 °C, which is a range of 0.6 °C. The uncertainty is half the range (0.6 / 2 = 0.3).
The value ± 0.3 °C represents the uncertainty of the mean value. It gives an indication of the confidence in the result and the spread of the data.\nIt is calculated from the range of the repeated measurements:\n- Highest value = 16.8 °C\n- Lowest value = 16.2 °C\n- Range = Highest - Lowest = 16.8 - 16.2 = 0.6 °C\n\nThe uncertainty is half the range:\nUncertainty = Range / 2 = 0.6 / 2 = 0.3 °C\n\nThis means the true value is likely to lie somewhere between 16.5 - 0.3 (16.2 °C) and 16.5 + 0.3 (16.8 °C).
Common mistakes
✗ Just saying "it makes it more accurate" without explaining what it represents.\n✗ Confusing uncertainty with error.
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