HW-1_solutions - Homework 1 Solution A temperature probe is...

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Homework 1 Solution A temperature probe is used to measure the temperature in an experiment. Before using the probe in the experiment, a calibration curve is needed to ensure the correct value to within the instrument accuracy. Using known temperature sources to calibrate the temperature probe, the following measurement results over multiple trials were conducted: 1. Determine the best-fit calibration line of the data. Display the results graphically, as well as the calibration equation. The data and best fit line is shown below and plotted True Temperature ( C ) Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 6 6.25 6.42 6.63 6.41 6.59 6.32 12 12.7 12.7 12.5 12.2 12.4 12.4 18 18.2 18.3 18.4 18.7 18.3 18.6 24 24.6 24.3 24.5 24.7 24.4 24.2 30 30.6 30.3 30.4 30.5 30.3 30.2 36 36.6 36.3 36.2 36.4 36.3 36.3 42 42.2 42.6 42.3 42.4 42.7 42.5 48 48.4 48.5 48.3 48.7 48.7 48.6 54 54.3 54.5 54.3 54.4 54.5 54.5 60 60.6 60.3 60.3 60.3 60.2 60.4 y = 0.999x + 0.450 R² = 0.9999 0 10 20 30 40 50 60 70 0 20 40 60 80 Measured Temperature (C) True Temperature (C) Temperature Calibration Chart Measured Calibration Fit
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2. What is the overall static sensitivity of the temperature measurement system? The static sensitivity of the system is the slope of the calibration curve. Reading from the calibration equation this is .999 (deg C measured / deg C True). If the calibration was perfect the slope would be 1. 3. Determine the accuracy limits of the temperature probe The accuracy limits are determined by creating a deviation chart, displaying the real value minus the (true) calibration value for each data point. The deviation chart is shown below. From the deviation chart, the limits of accuracy are -0.238 C and 0.298 C 4. Determine the systematic error of the probe The systematic error is the average of the reading minus the true values. In this case, each nominal temperature has its own systematic error: -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0 10 20 30 40 50 60 70 Deviation Temperature (C) Deviation Chart
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5. How could the systematic error estimation be improved? The systematic error could be error estimation could be improved by recalibrating the instrument, or by using a more accurate temperature measurement system.
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