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The uncertainty in reading a laboratory thermometer is 0.5 ∘ C. The temperature of a liquid falls from 20 ∘ C to 10 ∘ C as measured by the thermometer. What is the percentage uncertainty in the change in temperature?

A. 2.5%
B. 5%
C. 7.5%
D. 10%

User Ball
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2 Answers

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Final answer:

The percentage uncertainty in the temperature change is 10%.

Step-by-step explanation:

To find the percentage uncertainty in the change in temperature, we need to calculate the absolute uncertainty in the temperature change and then divide it by the actual change in temperature.

The absolute uncertainty in the temperature change is the sum of the absolute uncertainties in the initial and final temperatures.

Given that the uncertainty in reading the thermometer is 0.5°C and the temperature falls from 20°C to 10°C, the absolute uncertainty in the temperature change is 0.5°C + 0.5°C = 1.0°C.

The actual change in temperature is 10°C. Therefore, the percentage uncertainty in the temperature change is (1.0°C / 10°C) * 100% = 10%.

User James Aylett
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2 votes

Final answer:

To find the percentage uncertainty for a temperature change from 20 °C to 10 °C with an individual reading uncertainty of ±0.5 °C, you calculate the total uncertainty (1.0 °C), divide by the total temperature change (10 °C), and multiply by 100%, which results in a 10% uncertainty.

Step-by-step explanation:

The question revolves around determining the percentage uncertainty when measuring temperature changes with a laboratory thermometer. Since the uncertainty is a constant ±0.5 °C (meaning the reading could be 0.5 °C less or more than the displayed value), the total uncertainty for the change in temperature from 20 °C to 10 °C would be twice the uncertainty of an individual measurement because two separate readings are involved (initial and final). Therefore, the total uncertainty is 0.5 °C + 0.5 °C = 1.0 °C.

To find the percentage uncertainty, we divide the absolute uncertainty by the absolute change in temperature and multiply by 100%. The change in temperature is the final temperature minus the initial temperature, which is 10 °C - 20 °C = -10 °C (we use the absolute value, so it's just 10 °C). Therefore, the percentage uncertainty is (1.0 °C / 10 °C) × 100% = 10%.

The correct answer is D. 10%.

User HoshiKuzu
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