Slowing Down

Warning!  This pushes the limits of every thermodynamic term and principle ever published.  I tend to leap ahead and skip steps I consider obvious.  That is not good for explaining things, but great for solving puzzles.  So let's take a step back and slow down.

If you have two objects in an insulated box that are in thermodynamic equilibrium with each other, they will be in thermodynamic equilibrium with the ambient conditions outside of the box.  If 50% of the objects are at one temperature or energy level higher than the rest, they determine the steady state condition of the thermodynamic equilibrium.  So if the energy flux from the warmer half  to the cooler half is 100Watts, the energy flow from the total of the interior to ambient will be 100Watts.  You can vary the percentages anyway you like, the warmer will still determine the steady state condition if the system is in equilibrium.  If you add insulation to the box, the energy flow from warmer to colder will increase proportionally to the decrease in energy flow to ambient until equilibrium between the interior objects is restored.

Why is that statement correct?  If the two objects are in thermodynamic equilibrium, removing the insulation would not change their equilibrium for a finite period of time.  If there was 100Wm-2 flowing from one to the other, there would still be 100Wm-2 flowing once the insulation is removed.  Removing the insulation would cause both objects to emit more energy elsewhere, but they would remain in equilibrium with each other.  The steady state flow rate would gradually decrease if they had large thermal mass, more quickly if they had small thermal mass, but the equilibrium would remain.  This is conditional equilibrium or equilibrium dependent on balanced steady state conditions.

The chart above is the sensitivity of that box to an addition of 3.7Wm-2 of additional insulation equivalent.  The higher the highest temperature, the lower the impact.

Slowing Down Part II