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A thermometer reads 25.0 °C with an uncertainty of ±0.5 °C. If this temperature

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Question: A thermometer reads 25.0 °C with an uncertainty of ±0.5 °C. If this temperature is used in a calculation, what is the uncertainty in the result if the temperature is multiplied by 2?

Options:

  1. 1 °C
  2. 0.5 °C
  3. 0.25 °C
  4. 0.1 °C

Correct Answer: 1 °C

Solution: 

When multiplying, the relative uncertainty doubles: 2 * 0.5 °C = 1 °C.

A thermometer reads 25.0 °C with an uncertainty of ±0.5 °C. If this temperature

Practice Questions

Q1
A thermometer reads 25.0 °C with an uncertainty of ±0.5 °C. If this temperature is used in a calculation, what is the uncertainty in the result if the temperature is multiplied by 2?
  1. 1 °C
  2. 0.5 °C
  3. 0.25 °C
  4. 0.1 °C

Questions & Step-by-Step Solutions

A thermometer reads 25.0 °C with an uncertainty of ±0.5 °C. If this temperature is used in a calculation, what is the uncertainty in the result if the temperature is multiplied by 2?
Correct Answer: 1 °C
  • Step 1: Identify the measured temperature and its uncertainty. The temperature is 25.0 °C and the uncertainty is ±0.5 °C.
  • Step 2: Understand that when you multiply a value, the relative uncertainty also changes. Here, we will multiply the temperature by 2.
  • Step 3: Calculate the relative uncertainty. The relative uncertainty is the uncertainty divided by the measured value: 0.5 °C / 25.0 °C = 0.02 (or 2%).
  • Step 4: When multiplying by 2, the relative uncertainty doubles. So, we take the relative uncertainty of 2% and double it: 2 * 0.02 = 0.04 (or 4%).
  • Step 5: Now, calculate the new absolute uncertainty. The new absolute uncertainty is 4% of the new value (which is 25.0 °C * 2 = 50.0 °C). So, 0.04 * 50.0 °C = 2.0 °C.
  • Step 6: Therefore, the uncertainty in the result when the temperature is multiplied by 2 is ±2.0 °C.
  • Uncertainty Propagation – Understanding how uncertainties in measurements affect the results of calculations, particularly when using multiplication or division.
  • Relative Uncertainty – The concept that when multiplying a measured value, the relative uncertainty is considered, which can lead to an increase in the absolute uncertainty.
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