The discussion focuses on calculating the uncertainty in the cooling constant (k) using Newton's law of cooling, specifically the equation T(t) = T_A + (T_0 - T_A)e^(-kt). Participants analyze the impact of temperature uncertainties of +/- 0.5 degrees on the calculation of k. The method involves using logarithmic properties to determine uncertainty in ln(T(t) - T_A) and applying root-sum-square approaches for combining uncertainties. The conversation emphasizes the distinction between engineering tolerances and scientific uncertainty calculations.
PREREQUISITESStudents in physics or engineering, researchers dealing with temperature measurements, and anyone involved in uncertainty analysis in scientific experiments.
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?)