So this is where I write a long rant about thermal dynamics, and 
somebody comes along to tell me how completely wrong I am...

My mum's old oven was always too hot. It would burn anything you tried 
to cook to a cinder. My mum remains convinced this is because the 
thermostat was faulty. This is nonesense because... IT DOESN'T HAVE A 
THERMOSTAT.

The temparature control on the front just adjusts the size of the flame 
(by adjusting how fast the gas is let in). There's no temparature sensor 
beyond the one used to check that the gas has ignited.

I've told her this repeatedly. Her responce has always been "oh yeah? So 
how come the oven doesn't just constantly heat up until it melts?"

The answer, of course, is: BECAUSE IT'S NOT A PERPETUAL MOTION MACHINE!

This afternoon, I sat down and worked out the whole thing. See, you 
light a fire in the back of the oven, and it injects heat at a constant 
rate. An oven is well insulated - that's why even with a relatively tiny 
flame, it can reach a few hundred degrees Centigrade inside. But any hot 
object inevitably looses heat.

As the oven gets hotter, it looses heat faster. Eventually, the rate at 
which heat is lost equals the rate at which the flame is adding heat. At 
this point, the oven now holds a constant temparature. No thermostat 
required.

Adjusting the size of the flame changes the rate of heat injection, and 
hence moves the steady-state temparature.

It's the same physics that causes an object to reach terminal velocity 
in freefall, and why your car doesn't have an infinite top speed.

"Oh yeah? So how come the central heating system has a thermostat then?"

Well, our oven adjusts temparature by changing the size of the flame. 
The boiler for the heating does NOT adjust the size of the flame - only 
the duty cycle. Switching a flame on and off requires a thermostat.

More importantly, the inside of an oven is a few hundred degrees hotter 
than the outside. If the outside temparature moves 10 degrees, it's not 
going to change the steady-state temparature inside by much. On the 
other hand, the temparature outside your house is normally much closer 
to the temparature inside. So variations in outside temparature will 
have a bigger effect.

On top of that, it doesn't really matter if your oven is 10 degrees 
colder than you asked for, but it makes a pretty important difference if 
your house is. So an oven needs less exact control than a house, and a 
house has more significant variations to take into account.

I notice that electric cookers also use a thermostat. Again, this 
appears to be because they modulate duty cycle rather than heat 
injection rate, for whatever reason. (I presume it's just awkward to 
smoothly adjust the level of a multi-kW electric pathway?)

Small question: The rate at which an object looses heat. Clearly this is 
proportional to how much hotter it is than its surroundings. But is this 
relationship linear?

 From what I can remember, the temparature of an object approaches that 
of its surroundings according to an exponential curve ("cooling curve"). 
The derrivative of an exponential is also an exponential, so that would 
indicate that as an object gets hotter, it looses exponentially more 
heat. Right?

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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