Orchid XP v8 wrote:
> 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?

No.  The radiation of energy due to heat is proportional to the fourth 
power of the absolute temperature.

Regards,
John

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>> 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?
> 
> No.  The radiation of energy due to heat is proportional to the fourth 
> power of the absolute temperature.

And how about the conduction and/or convection of heat as a function of 
temparature difference?

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

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>> No.  The radiation of energy due to heat is proportional to the fourth 
>> power of the absolute temperature.

Also your item receives radiation from other objects nearby, and of course 
the amount depends on the temperature of them.

> And how about the conduction and/or convection of heat as a function of 
> temparature difference?

Conduction is linear with temperature difference, convection is more complex 
because it involves fluid flow.

Also, bear in mind that the thermal properties (specific heat, conductivity, 
emissivity) will change significantly with temperature, so it is really hard 
to give a straightforward function of temperature.

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>> Now I simply *must* know if the specific heat capacity of oil is 
>> significantly different from water...
> 
> I think it's actually lower than water.

According to Wikipedia (which, obviously, is never wrong), the specific 
heat of water is about 4.1 J per g per degree, whereas for parafin wax 
(the only organic compound I could find) it's 2.2 - roughly half.

I'd be interested to know what it is for typical animal fat. And also 
for sugar, actually.

At this point, I hypothesize that these substances remain hotter than 
hot water due to the lack of evatorative cooling...

>> (Every time I make cheese toasties, the cheese inside is hotter than 
>> lava! They should fill storage heaters with that stuff or something...)
> 
> They use it for storage heaters and cooling electrical stuff because it 
> doesn't boil at 100 degrees and is an insulator.

I would imagine the fact that it doesn't corrode metal is a fact too... ;-)

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

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>>> No.  The radiation of energy due to heat is proportional to the 
>>> fourth power of the absolute temperature.
> 
> Also your item receives radiation from other objects nearby, and of 
> course the amount depends on the temperature of them.

Which, I presume, means an object at thermal equilibrium emits and 
absorbs equal amounts of radiation.

>> And how about the conduction and/or convection of heat as a function 
>> of temparature difference?
> 
> Conduction is linear with temperature difference, convection is more 
> complex because it involves fluid flow.
> 
> Also, bear in mind that the thermal properties (specific heat, 
> conductivity, emissivity) will change significantly with temperature, so 
> it is really hard to give a straightforward function of temperature.

OK. Well when I did some simple experiments at school, we found that a 
glass of boiling water apporaches thermal equilibrium more or less 
logarithmically. So I think we can safely conclude that thermal losses 
increase at least linearly with temparature - even if the exact function 
is hard to pin down.

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

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Invisible wrote:

> According to Wikipedia (which, obviously, is never wrong), the specific 
> heat of water is about 4.1 J per g per degree, whereas for parafin wax 
> (the only organic compound I could find) it's 2.2 - roughly half.

Actually, 2.5 for parafin wax, 2.2 for ethane, and 2.2 for gasoline. So 
the only three organic substances present show a remarkable [and quite 
possibly coincidental] correlation.

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

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> Which, I presume, means an object at thermal equilibrium emits and absorbs 
> equal amounts of radiation.

Yes, in a vacuum.  In air or with some other material contact, you need to 
include the conduction of heat too.

> OK. Well when I did some simple experiments at school, we found that a 
> glass of boiling water apporaches thermal equilibrium more or less 
> logarithmically. So I think we can safely conclude that thermal losses 
> increase at least linearly with temparature - even if the exact function 
> is hard to pin down.

Water is very stable thermally, for example it's specific heat varies by 
less than 1% from 0 to 100 degrees.  Other materials are far more unstable, 
and when you have several materials together in a system it is even more 
complex.  Then add in that your heat source may be generating different 
amounts of heat at different temperatures, and things are far from linear 
once you get away from simple science experiments.

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> I would imagine the fact that it doesn't corrode metal is a fact too... 
> ;-)

So long as it's sealed there isn't (any significant) corrosion.  I imagine 
the heating system you have at home has been working for several years, 
probably several decades with water running round it the whole time.

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scott wrote:
>> I would imagine the fact that it doesn't corrode metal is a fact 
>> too... ;-)
> 
> So long as it's sealed there isn't (any significant) corrosion.  I 
> imagine the heating system you have at home has been working for several 
> years, probably several decades with water running round it the whole time.

Actually no, it was fitted about 3 years ago. ;-)

What I *have* observed is that the water inside such systems is always 
jet black, and usually stinks like hell...

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

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Invisible wrote:
>>> Now I simply *must* know if the specific heat capacity of oil is 
>>> significantly different from water...
>>
>> I think it's actually lower than water.
> 
> According to Wikipedia (which, obviously, is never wrong), the specific 
> heat of water is about 4.1 J per g per degree, whereas for parafin wax 
> (the only organic compound I could find) it's 2.2 - roughly half.
> 
> I'd be interested to know what it is for typical animal fat. And also 
> for sugar, actually.
> 


Soybeans, which was the only usable result google gave me for "specific 
heat of oil", have a specific heat of about 1.926 to 2.912 kj/kg-K 
according to 
http://www.blackwell-synergy.com/doi/abs/10.1111/j.1745-4530.1999.tb00500.x

Sugar, according to 
http://209.85.215.104/search?q=cache:B3m5sDbitg0J:www.solexthermal.com/assets/pdf/en/SolexCS_The%2520Solex%2520Heat%2520Exchanger%2520-%2520A%2520Better%2520Way%2520to%2520Cool%2520Sugar%2520Crystals.pdf+%22specific+heat+of+sugar%22&hl=en&ct=clnk&cd=4&gl=us,


kilo calorie is 4.185 Joules).

And, for other chemicals, 
http://www.engineeringtoolbox.com/specific-heat-fluids-d_151.html is a 
good table.

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