I'm just ready to begin kinematics and the math teacher with whom I
share a class is beginning slope. There is a problem in the Calculus
book (Thomas 9th ed.?) that shows a graph of the temperature in an
insulating material (cross section of a wall) vs position in the wall
(warm inside and cold out). In some of the wall components (gypsum for
example) the temperature falls slowly (low slope) while in another area
(fiberglass) the temperature falls off more quickly (greater slope).See
below.
Question: Which is the better insulator? That is how does one interpret
the *physical meaning* of the slope (degrees/inches)?
The key says the low slope material. But if I pick up a hot drink in a
well insulated container I'll have a large temperature difference
between the outside and inside. (Seems like a steep slope.)
Does the equation for rate of heat flow (OUCH!...that's what Giancoli
calls it. _Physics_, 4th ed. p. 411) apply?
dQ/dt = kA (T1 - T2) / L
where k is the thermal conductivity, A is area, and L is thickness.