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RV Maintenance
Thermal HalfLife

In all my work of insulating the RV, I have been working with thermal entropy: The simple and basic Law of Cooling.

eq-ChangeProp.gif, 4.0kB
But it is not the only differential equation that expresses the notion of Rate of Change that is proportional to the Amount of that which is changing. Here, the negative sign indicates that Y is decreasing, and that my RV is cooling down.

eq-ChangePropSolut.gif, 7.7kB
The solution is straight foreward.

Eq-TempDecayBasic.gif, 5.7kB
Here, in my case, I have added an offset (abient outside temperature).

Eq-B-kbt500.gif, 4.3kB
In previous pages, I developed the R value, as used in insulation materials. R values are convenient, and used throughout the industry. Time time constant k is also convenient. But there is yet another way to express this decay function with a constant. A third way...

And that notion is one of "HalfLife". Normally, Half-Life is a term used in radioactive decay. For example the Neutron will decay into three particles, a Proton, Electron and Neutrino, in 14.7 minutes. I assert, sense mathematics can not tell the difference between Thermal Entropy and particle decay, that there IS no difference; BOTH are Entropy.

I have established in previous pages that: My RV has an Rval= -6.95 units: area x degree x time/BTU
My RV has a time constant k=-0.1269 units:t-1
And they are equivalent, in that they express the same time constant.

eq-HalfLife.gif, 10kB
There is yet a third way to express this same time constant.
Dividing the natural log of two by my RV time constant k gives:
5.4622 Hours
In my RV, it takes 5.4 hours for the temperature to drop one half of the temperature difference. And another 5.4 hours to drop half of that difference. And so on.

HalfLife5466.gif, 2.9kB This is so much easier to remember than ether the -0.13 k value,
or the -6.95 R-value.
Wow! This is convenient!