A Levels Physics

A thermometer can be read to an accuracy of ±0.5°C. This thermometer is used to measure a
temperature rise from 40 °C to 100°C.
What is the percentage uncertainty in the measurement of the temperature rise?
A 0.5%
B 0.8%
C 1.3%
D 1.7%


Choice D is correct because:

The temperature rise is calculated by subtracting the initial temperature from the final temperature: 

Temperature rise = Final temperature - Initial temperature = 100 °C - 40 °C = 60 °C

The maximum possible value for the temperature rise is by adding the maximum positive uncertainty (+0.5 °C): 

Maximum temperature rise = Temperature rise + Maximum uncertainty = 60 °C + 0.5 °C = 60.5 °C

The minimum possible value for the temperature rise is by subtracting the maximum negative uncertainty (-0.5 °C): 

Minimum temperature rise = Temperature rise - Maximum uncertainty = 60 °C - 0.5 °C = 59.5 °C

Now, calculate the range of possible values for the temperature rise: 

Range = Maximum temperature rise - Minimum temperature rise = 60.5 °C - 59.5 °C = 1 °C

Finally, calculate the percentage uncertainty by dividing the range by the temperature rise and multiplying by 100: 

Percentage uncertainty = (Range / Temperature rise) × 100 = (1 °C / 60 °C) × 100 ≈ 1.67%

This is closest to 1.7% which is choice D.

Choices A, B, and C are incorrect because they state incorrect percentage uncertainty in the measurement of the temperature rise.

Uncertainties in Measurement | 2014 - M/J - 9702/12 | Q5