/sci/ - Science & Math

>>9170269
the intuitive answer is, since the heat equation is
[math] \frac{\partial }{\partial t}u(x,t)= a\frac{\partial^2 }{\partial x^2}u(x,t) [math]
we expect bigger change in heat, wherever the heat gradient is bigger, meaning the nondilluted vessel will lose heat faster than the dilluted one.

I illustrated it for you in a numerical solution for the 1D heat equation.
the blue dotted line is the initial nondilluted solution, the red dotted line is the initial dilluted solution (half as hot, twice the volume)
the drawn out lines are the heat distributions after a fixed amount of time.
As you can see, the red and blue lines are almost identical. Once you dillute the blue line though, you will get the green distribution which is way lower than the red one