Ive been trying to work this question out on my own for over a week now and cant seem to crack it. I hope its in the right Sub forum and im really sorry if its not.
A hot metal body is allowed to cool in still air and the difference in temperature, θ (Celsius) between the body and its surroundings is recorded at, t (seconds) from the beginning of the cooling period.
its gives me the following:
The question asks me to verify graphically the relationship between θ and t is of the form: θ=θoe-kt (-kt is to the power of θoe) Hence estimate the values of the constants θo and k. Then using this relationship compile a table of values of θ for values of t between 0 and 600 at intervals of 60.
I have taken the natural log (ln) of each of the temperatures in the table above and plotted them in the graph. I drew a line of best fit and found the y intercept, and took the natural exponential of it which is:
e4.25 = 70.11
I think 70.11 is the initial temperature at time 0. so θo= 70.11?
Is k the gradient of the line? if so how do i calculate the values of θ?
All help is greatly appreciated, it would be amazing to get this out of the way!