The discussion revolves around determining the uncertainty in the constant k from Newton's law of cooling, specifically focusing on the uncertainties associated with temperature measurements. The relevant equation is provided, and participants are exploring how to calculate uncertainties in logarithmic functions and their implications for k.
There is an ongoing exploration of how to calculate uncertainties, with some participants suggesting different approaches based on engineering versus scientific perspectives. Guidance is sought on finding uncertainties involving logarithmic functions, and multiple interpretations of uncertainty are being considered.
Participants note that each temperature measurement has an uncertainty of +/- 0.5 degrees, and there is a request for approximate values for the temperatures involved. The discussion also highlights the necessity of showing attempts in line with forum rules.
You will also need approximate values for the temperatures.sunmoonlight said:Homework Statement: Uncertainty in Newton's law of cooling
Relevant Equations: T(t) = = 𝑇_𝐴+(𝑇_𝑜−𝑇_𝐴)𝑒^(−𝑘𝑡)
I'm finding the uncertainty of k, given that each temperature has an uncertainty of +/- 0.5 degress.
There are different concepts of uncertainty. An engineer worried about engineering tolerances would just look at the combinations of the extreme values. A scientist would take the given uncertainties as standard deviations in normal distributions and use root-sum-square approaches to combine them. I assume you are looking for the latter.sunmoonlight said:say the T(O) = 90 +/- 0.5, T(t): 60 +/- 0.5, TA = 10 +/- 0.5, temp difference (T(t) - TA) is 50 degrees +/- 0.5, t= 100s
1. Is the uncertainty for ln (T(t) - TA) = 1/2*(ln50.5 - ln49.5) = +/-0.01?
2. If you substitute the values into the eqt, you get k = (ln50/80)/-100, so what's the uncertainty for k (like how do you find uncertainty involving logs?)