# Math Help - Error Analysis on Temperature Difference Measurements

1. ## 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!

2. Originally Posted by wilsonudevil
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!
$\Delta DT = \Delta \overline{T}_2 + \Delta \overline{T}_1$.