# Thread: Newton's law of cooling

1. ## Newton's law of cooling

Newton's law of cooling leads to a mathematical model of the cooling of a hot cup of coffee. The temperature of the coffee at any time is given by the solution of the following differential equation

Find the general solution of the differential equation

Find the particular solution of the differential equation if initially, the temperature of the coffee is 83 degrees.

Find the temperature of the coffee when t = 4.3

How do I do this?

2. ## Re: Newton's law of cooling

$\frac{dT}{dt}+ 0.2T- 5= 0$ is the same as $\frac{dT}{dt}= 5- 0.2T$.
Changing to differential form $\frac{dT}{5- 0.2T}= dt$. Can you integrate those?

3. ## Re: Newton's law of cooling

Originally Posted by leonm92
Newton's law of cooling leads to a mathematical model of the cooling of a hot cup of coffee. The temperature of the coffee at any time is given by the solution of the following differential equation

Find the general solution of the differential equation

Find the particular solution of the differential equation if initially, the temperature of the coffee is 83 degrees.

Find the temperature of the coffee when t = 4.3

How do I do this?
separation of variables ...

$\frac{dT}{dt} = 5 - 0.2T$

$\frac{dT}{dt} = 0.2(25 - T)$

$\int \frac{dT}{25-T} = \int 0.2 \, dt$

finish it and get temperature $T$ as a function of time $t$ ...

4. ## Re: Newton's law of cooling

to be honest, I haven't got a clue about integrating

5. ## Re: Newton's law of cooling

Originally Posted by leonm92
to be honest, I haven't got a clue about integrating
then it's obvious you are ill prepared to tackle this problem ... here is a link for a place to start

Indefinite Integrals Part 1 | Khan Academy Calculus Lecture

6. ## Re: Newton's law of cooling

Originally Posted by leonm92
to be honest, I haven't got a clue about integrating
It is not a good idea to take differential equations until after you have learned calculus.