In all my work of insulating the RV, I have been working with thermal entropy:
The simple and basic Law of Cooling.
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.
The solution is straight foreward.
Here, in my case, I have added an offset (abient outside temperature).
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...
The third way...
And that notion is one of "HalfLife".
Normally, HalfLife 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,
then there IS no difference; BOTH are Entropy. Mathematically there is no difference!
I am free and justified to use Half Life for my RV.
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)
The two notions are equivalent, in that they express the same decay activity.
They must, because in both notions, there are only two terms in the exponent: a "t", and a "k".
There is yet a third way to express this same time constant:
Instead of a "generic" time constant, that fits all circumstances,
use a specific time constant called a "HalfLife" time constant that refers to half the "stuff".
...And it is easy to get.
Dividing the natural log of a half 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 another 5.4 hours to drop half of that difference.
And so on...
This is too damn easy!
This is so much easier to remember than ether the -0.13 k-value,
or the -6.95 R-value.
I am so happy that I have derived and discovered this.
Wow! This is convenient!
This is so much easier to remember than ether the -0.13 k-value,