> It is something usually mentioned in engineering school, though not usually as a joke so much as a matter of practicality.

Understood...

>
> So when, exactly, do these simplifications apply? Whenever a practical need arises, like my water for making bread example above. In general, the application is made to real world systems. As I implied with the water example, there are numerous variables in the real world which will affect a system. Most scientific studies make use of simplifying assumptions, such as the infinitely large room with a constant temperature of 20ºC. However, a real room with people moving around in it and weather conditions changing outside (as well as numerous other imfluences) will always be in a state of temperature flux, even if only by a thousandth of a degree per second.

Oh, I misunderstood your original statement then. All you meant is that normal room temperature fluctuations ensure that the cup of liquid will never ever reach perfect equilibrium. True. However, I am still puzzled by why you even bother to frame the question in terms of "infinitely long duration," or, as in your current example, "an infinitely large room." To make those assumptions seems unrealistic in the first place -- unless the engineer is doing a seat-of-the-pants, super-simplified calculation which required infinite time or infinite space to go to completion. Surely an engineer trying to strive for reasonable accuracy would posit an *enclosed* space for a room, and maybe even a thermal gradient of heat absorption/reflection radiating from the room's walls, plus a possible contribution due to draft current from a forced-air furnace convection, etc. What I'm trying to say is that if engineers go for the practical, wouldn't they look at the real-world situation rather than try to set up for the infinite situation.


> Don "OK, that was maybe a bit much. Sorry." Monkey

Are you kidding? "Solve the World" equations, situations, and parameters are absolutely FASCINATING. :-)

Wolfspirit