So we know d
ΔΩ
q =
q(Txi,Txf) incertainty for the quadratic fit and d
ΔΩ
l =
l(Txi,Txf) for the linear fit. (Those functions are too awful to be written here, if you really want them, click here)
Since f(Txi,T
xf)>q(
Txi,T
xf)>l
(Txi,T
xf),
we can say that the trues rise of temperature is given by the linear
fit (the simplest solution), with an error equal to f(Txi,T
xf)+q(
Txi,T
xf). (if you disagree or don't understand, click
here to have more explanations, word format)
We can now plot the function for the total uncertainty : t(
Txi,T
xf) = (f(
Txi,T
xf) + q(
Txi,T
xf) + l(
Txi,T
xf))/r(
Txi, T
xf) that gives us :
where r(
Txi, T
xf) is the rise of temperature with the linear or the quadratic fit
and you can show (for a rise of temperature bigger than 10°C)
the relative error in the measurement of the difference in temperature
is smaller than 4.8%, that is smaller than the error budget for the
temperature (budget of 1%, reached for a rise in temperature bigger than 1.5°C).
So that's great ^^, we don't realy need to know whether th fit is
quadratic or linear,
The formula to measure a rise of temperature is :
0.9657*(Txf
-Txi
) +/- 0.5% (if T
xf-T
xi > 10°C) where T
xf is the final temperature and T
xi the initial one,
both measured with the same rtd.
Something hazy ? Need more explanations? contact
yannick rousseau <rousseau@jlab.org>