Newtons Law of Cooling

1. Feb 19, 2008

Grapz

1. The problem statement, all variables and given/known data
The equation dQ/dt = k ( T - Troom) is newtons law of cooling. dQ/dT being the rate of heat loss. I want to convert this equation to dT/dt, the rate of temperature decay. How do i go about doing this?

2. Relevant equations

3. The attempt at a solution

Is Q proportional to T? then i can just sub it in for Q and solve for the differential equation?

2. Feb 19, 2008

cepheid

Staff Emeritus
Well, Q is not proportional to T. Here's what I did:

$$\frac{dQ(t)}{dt} = k(T(t)-T_0)$$

$$\frac{1}{k}\frac{dQ(t)}{dt} +T_0 = T(t)$$

$$\frac{d}{dt}T(t) = \frac{1}{k}\frac{d^2Q(t)}{dt^2}$$

3. Feb 19, 2008

cepheid

Staff Emeritus
To me, it seems like you need T(t) to solve for Q(t). But if you already had T(t), then you could just get T'(t) by direct computation. You don't have it though...