Thread: Newton's Law of Cooling Derivation

x(t) = Temperature of an object at time t.
(k < 0)
T = surrounding cooler temperature.

Given:
(dx/dt) = k(x(t) - T)

Derive using differential equations and show it equals:
x(t) = T + Ce^kt
Where C is a constant.


Attempt:
dx = k(x(t) - T) dt

Then integrate both sides?

If you are trying to separate the variables then pull x(t) onto the LHS with dx.

You cannot integrate x(t) with respect to t because you do not yet know what specific function of t x is.
As Chi Sigma says, you can "pull x(t) onto the LHS with dx" and integrate


Note that T is a constant.

Originally Posted by HallsofIvy

As Chi Sigma says,

I wish I was that good with D.E.s! ;-)