View source for Determining the ultimate temperature of a solar cooker

Assume the temperature inside the cooker acts as that of a finite object surrounded by an infinite object at the ultimate temperature. Then the net power into the cooker is proportional to the difference in temperature between the inside of the cooker and the surroundings at the ultimate temperature (not the ambient temperature).
:P1=α(Tu-T1)
:P1=power now, α=undetermined constant, Tu=ultimate temperature, T1=temperature now.
Using the subscript 2 to denote the power and temperature measured at a later time:
:P2=α(Tu-T2)
:P1=α(Tu-T1)
:Tu=T1+P1/α
Substituting α=P2/(Tu-T2) into Tu=T1+P1/α, we get:
:Tu=T1+(P1/P2)(Tu-T2)
Solving for Tu:
:Tu=T1+(P1/P2)Tu-(P1/P2)T2
:Tu-(P1/P2)Tu=T1-(P1/P2)T2
:Tu(1-P1/P2)=T1-(P1/P2)T2
:1-P1/P2=(P2-P1)/P2
:Tu=(P2T1-P1T2)/(P2-P1)
In a solar cooker, the temperature can be measured by a thermometer, better a precise, datalogging instrument. If the specific heat capacity of the contents are known, then the net input power can be determined from the change in temperature and the mass of the contents:
:P=∆T*C*m/∆t
P=net input power, ∆T is change in power over some small amount of time, C is specific heat capacity of contents, m is mass of contents, and ∆t is that small amount of time. Because of the discrete limits of precision of the thermometer or datalogger, temperatures should be smoothed, or the resulting power should be smoothed for analysis.

[[Category:Solar cooking]]