Measurement correction and uncertainty

[urh]

Give a measurement result by the correction and uncertainty in the calibration of the thermometer indicator! With reference thermometer are measured 135.14 ° C, with another thermometer which was calibrated with reference we got the following values: 140.15 ° C 140.14 ° C 140.13 ° C 140.12 ° C 140.11 ° C 140.12 ° C, 140.13 C, 140.14 C, 140.12 C, 140.13 ° C. The uncertainty of the reference thermometer is 0.05 ° C, the uncertainty of the bath in which you calibrated amounts to 0.07 ° C

I am asking for solution, how to solve the problem.

Thanks for help.

 

[jbsteele]

The corrected measurement result of the thermometer indicator after calibration is: 140.125 °C ± 0.105 °C. The uncertainty was determined by combining the uncertainties of the reference thermometer (0.05°C) and the bath (0.07°C).

 

[nlightner]

I understand the importance of accurate measurements and the impact that measurement correction and uncertainty can have on scientific data. In the case of the thermometer indicator, the correction and uncertainty in the calibration process can greatly affect the final measurement result.

In this situation, we have two sets of measurements - one from a thermometer calibrated with a reference thermometer, and another from a reference thermometer itself. The measurements from the calibrated thermometer are consistently higher than those from the reference thermometer, indicating a potential error in the calibration process.

To address this issue, we need to first determine the correction factor that needs to be applied to the measurements from the calibrated thermometer. This can be done by taking the average of the difference between the two sets of measurements, which in this case is 0.05 °C. This means that the calibrated thermometer consistently reads 0.05 °C higher than the reference thermometer.

Next, we need to consider the uncertainty of the reference thermometer and the bath in which the calibration was done. The uncertainty of the reference thermometer is given as 0.05 °C, which means that the actual temperature could be anywhere within a range of 0.05 °C above or below the measured value. Similarly, the uncertainty of the bath is given as 0.07 °C, which means that the actual temperature in the bath could be anywhere within a range of 0.07 °C above or below the set temperature.

Taking all of this into account, we can provide a measurement result that accounts for both the correction factor and the uncertainties. The corrected measurement from the calibrated thermometer would be 140.09 °C (140.14 - 0.05). However, to account for the uncertainties, we must also provide an uncertainty range. This would be ±0.12 °C, taking into account the uncertainties of both the reference thermometer and the bath.

In conclusion, the corrected measurement from the calibrated thermometer is 140.09 °C ± 0.12 °C. This provides a more accurate and reliable measurement result, taking into account the correction factor and uncertainties in the calibration process.