Converting Newton's Law of Cooling from Heat Loss to Temperature Decay

[Grapz]

Homework Statement

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?

Homework Equations

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?

 

[cepheid]

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

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

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

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

 

[cepheid]

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...