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sunmoonlight
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- 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.
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?)
Newton's law of cooling is a mathematical equation that describes the rate at which an object cools down in a surrounding environment. It states that the rate of change of temperature of an object is directly proportional to the difference between its temperature and the temperature of its surroundings.
Uncertainty in Newton's law of cooling refers to the potential error or inaccuracy in the measurements or calculations used to determine the rate of cooling. This can be caused by various factors such as measurement limitations, experimental errors, and environmental fluctuations.
Uncertainty in Newton's law of cooling can be calculated using various statistical methods such as standard deviation, confidence intervals, and error propagation. These methods take into account the variability and potential sources of error in the measurements and calculations to determine a range of possible values for the uncertainty.
The presence of uncertainty in measurements and calculations can affect the accuracy and precision of the results obtained from Newton's law of cooling. A high level of uncertainty can indicate that the data is not reliable and may need to be reevaluated or improved upon to increase the validity of the law.
To minimize uncertainty in Newton's law of cooling, it is important to carefully control and monitor the experimental conditions, use accurate and precise measurement equipment, and perform multiple trials to reduce random errors. Additionally, using more advanced statistical techniques and considering potential sources of systematic error can also help to minimize uncertainty.