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Math Help - Error Analysis on Temperature Difference Measurements

  1. #1
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    Question Error Analysis on Temperature Difference Measurements

    Hi all,

    Having a slight problem with working out the uncertainty on one of my results.
    I'm measuring the water temperature before and after it passes through a heat exchanger.
    Measurements are made with 2 type K thermocouples attached to a pico TC-08 data logger.
    Now I'm interested in the temperature difference and the uncertainty on it.

    Here's my method...

    1. I connect a thermocouple to each part of the pipe where I want to take the water temperature (before (T1) and after (T2) the heat exchanger).
    2. I wait until the temperatures have stabilised and then I begin to take my measurements.
    3. I record the temperatures every 5 seconds for 30 minutes giving me 360 measurements for each temperature.
    4. I then take the mean temperatures so T1_bar and T2_bar
    5. I then find the temperature difference DT (so T2_bar - T1_bar)

    So my question is this: What is the uncertainty on DT?

    The thermocouples are accurate to +/-1K and the datalogger to +/- 0.25K
    If I combine the error from the data logger and the thermocouple by adding them in quadrature I get quite a large uncertainty which isn't much good when measuring small temperature differences. Should I be using standard deviations since I have a fairly large sample?

    Any help much appreciated!
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  2. #2
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    Quote Originally Posted by wilsonudevil View Post
    Hi all,

    Having a slight problem with working out the uncertainty on one of my results.
    I'm measuring the water temperature before and after it passes through a heat exchanger.
    Measurements are made with 2 type K thermocouples attached to a pico TC-08 data logger.
    Now I'm interested in the temperature difference and the uncertainty on it.

    Here's my method...

    1. I connect a thermocouple to each part of the pipe where I want to take the water temperature (before (T1) and after (T2) the heat exchanger).
    2. I wait until the temperatures have stabilised and then I begin to take my measurements.
    3. I record the temperatures every 5 seconds for 30 minutes giving me 360 measurements for each temperature.
    4. I then take the mean temperatures so T1_bar and T2_bar
    5. I then find the temperature difference DT (so T2_bar - T1_bar)

    So my question is this: What is the uncertainty on DT?

    The thermocouples are accurate to +/-1K and the datalogger to +/- 0.25K
    If I combine the error from the data logger and the thermocouple by adding them in quadrature I get quite a large uncertainty which isn't much good when measuring small temperature differences. Should I be using standard deviations since I have a fairly large sample?

    Any help much appreciated!
    \Delta DT = \Delta \overline{T}_2 + \Delta \overline{T}_1.
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