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 °C
0.5 °C
0.25 °C
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.
