Calculating Temperature Uncertainty - Help Needed!

[JoshMG]

I have a lab and I'm having a hard time calculating or even understanding how to calculate the uncertainty.

It wants me to calculate the uncertainty of temperature.

Here is my data:
time (mins) Temp (°C)
2 23.2
4 26
6 29
8 31.5
10 33.5
12 35.5
14 37.6
16 39.7
18 41.8
20 43.9

Don't I need some given value and divide the average by it? And I also don't understand how I'm suppose to calculate the uncertainty when the readings of the temperature was taken at different times...
Help! Am I going crazy or did I do my lab wrong?

 

[cepheid]

Can you give the EXACT wording of the question in your lab assignment that asks about uncertainty?

EACH temperature value has an uncertainty associated with it due to the fact that your measuring instrument is not infinitely precise. In fact, your measuring instrument seems to be precise only to a tenth of a degree. Therefore, just as an example, you have no way of knowing whether the temperature at 8 minutes was 31.50 or 31.53 or ... whatever. The thermometer doesn't measure that finely.

In principle it could have been anywhere in the range of 31.45 to 31.54, (If it was an analog thermometer with tick marks, you'll assume the human being looking at it will try to figure out whether it was less than halfway between two ticks or more than halfway between them. If it was a digital thermometer, you assume it follows some reasonable quantization rules that correspond to our rounding rules.) This is one reason why a good rule of thumb is that the experimental error could be considered to be HALF the precision of the measuring instrument (0.05 degrees in this case). As a result, we'd express the temperature as:

$$31.5^{\circ} \textrm{C} \pm 0.05^{\circ} \textrm{C}$$

Anyway, can you see what the point of all of this estimation of experimental uncertainty is? Can you see that the precision of the thermometer limits how *certain* we can be about the actual temperature, and that the degree of certainty is expressed by the number of significant figures, and clarified by the experimental error that we tacked on?

 

[Moetasim]

Hello,

Calculating uncertainty in temperature involves determining the range of possible values that the temperature could fall within, given the limitations of the measuring equipment and the precision of the measurements. To calculate the uncertainty, you will need to use the formula:

uncertainty = (highest value - lowest value) / 2

In your case, you will need to first calculate the average temperature by adding up all the temperature readings and dividing by the number of readings. This will give you an average temperature of 34.16°C. Then, you will need to determine the highest and lowest values in your data set, which are 43.9°C and 23.2°C, respectively. Plugging these values into the formula, you will get an uncertainty of 10.35°C.

It is important to note that the uncertainty in temperature is affected by the precision of the measurements. In your data set, the temperature readings are given in whole numbers, meaning that the precision is limited to the nearest degree. This means that the uncertainty calculated using the formula above may not be entirely accurate, as it assumes a precision of 0.1°C. If you want a more accurate uncertainty, you will need to consider the precision of your measurements and adjust the formula accordingly.

As for the different times at which the temperature readings were taken, this should not affect the calculation of uncertainty. As long as the temperature readings are accurate and precise, the uncertainty can be calculated using the highest and lowest values in the data set.

I hope this helps clarify the process of calculating uncertainty in temperature. It is always a good idea to double check your calculations and consult with your instructor if you are unsure about any aspect of your lab. Good luck!