Thursday, November 4, 2010 0

DCP, aspect 3:

Students seem to find this difficult to achieve a ‘c’. The aspect is looking for students to correctly present their final answer (to the correct number of significant figures) and to display an uncertainty / error value (to the correct number of significant figures).

We will consider each part separately:

Firstly, the correct number of significant figures. The student should look back through all the data used in DCP aspect 1. The final answer should have the same number of significant figures as the smallest number of significant figures used in the calculation.

For example, in an enthalpy experiment, q = mcΔT, a student may use q = 1.007 x 4.18 x 4.50

The answer should be displayed to 2 significant figures as the smallest number of significant figures is three (ie, 2.50).

The sencond part concerns the propogation of errors or uncertainties:

Recall  that for DCP aspect 1 that raw data needs to be recorded with the appropriate uncertainty. Each uncertainty in the calculation needs to be converted into a % uncertainty. All the % uncertainties should be added together and expressed as both a % uncertainty of the final answer and also an absolute uncertainty of the final answer.

This is much easier to show as a calculation.

Using the above example of q = mcΔT

We have a mass of 1.007 + / – 0.001 and a temperature change of 2.5 + / – 0.1 oC

For mass, the % uncertainty is (0.001 / 1.007) x 100 = 0.0993%

For temperature change, the % uncertainty is (0.1 / 2.50) x 100 = 4%

The total % uncertainty is = 0.0993 + 4 = 4.0993%

Using the raw data values, the energy value is 1.045 x 4.18 x 2.50 = 10.92025  J, which is 10.9 J to 3 sf

So the final answer is 10.9  J + / – 4 %  as a % uncertainty. Why only 4 %? Well, the uncertainty needs to be to the same level of decimal places as the calculated value. An uncertainty of +/ – 4.1 % or + / 4.0993 % would be more accurate than the answer.

We then find what 4.0993 % of 10.9 comes to. This gives us an absolute unceratinty value.

So, 4.0993% of 10.9 J is 0.44 J, making the final answer 10.9J + / – 0.4 J (0.4 J and not 0.44 J to be of a consistent number of significant figures as the final answer).