Heat loss from an insulated water tank ----- Thermodynamics

[stoody]

Hi and thanks in advance for any help with this problem.

If I have a very very well insulated tank of water of say 4 litres.
If we could assume that the tank had no heat loss...
The tank is heated by an electrical device that generates say 2 watts of heat
Would the tank of water eventually boil or would the water in the tank dissapate some of the heat (somehow). If it would boil is it slower than a simple calculation of the energy put in by the heater would indicate?


it is for an idea I am trying to think through but short of making up a prototype and seeing what happens i am at a dead end.

Cheers Stoody

I hope asking a question on a first post is Ok

[Mapes]

Hi stoody, welcome to PF! Asking a question is totally fine; that's how many of us start here.

In general, the more insulation, the faster the water will heat up. If the container is vented so that pressure doesn't build up, the water will boil quickly and at 100°C. The minimum amount of time it would take to boil can be calculated from the power input and the specific heat of water (it's the minimum time because some thermal energy will always escape through the insulation).

If the container isn't vented, the problem becomes a little more complicated because the pressure buildup suppresses boiling. So boiling could occur at >100°C; this temperature can be estimate if you have an idea of the pressures involved. (Note that making a pressurized container in this way is dangerous; the container would eventually explode.)

[stoody]

Mapes, Thank you for your response. What I am driving at with my question is; would a very very small input of energy eventually boil a super insulated vessel or would things like the convection of the water in the vessel dissipate that heat (admitally very slowly) or is the convection movement sort of free of net energy input.

Another way to look at at my problem would be;say a mass of copper (say 4kg) again super insulated and again attached to a heat source of 2watts. Would it just keep heating up or is energy expended in vibrating the block (on a minute scale) I understand that in practical terms the insulation would leak a little of the heat.

Cheers and again thanks for your answer.
Stoody

[Mapes]

If the energy input is higher than the energy output, then the object or material will heat up; there's no way around it. Note, however, that heat loss through conduction and convection increases with temperature (and heat loss through radiation increases very quickly, to the fourth power of temperature), so you'll come to an equilibrium point soon enough where things are stable.

If you're interested in estimating this stable temperature, take a look at a good heat transfer book like Incropera and DeWitt's Fundamentals of Heat and Mass Transfer for information on conduction, convection, and radiation. (Or you can ask about it here, of course!)

[stoody]

Thank you (again) so much for your reply. I will look that up Fundamentals of Heat and Mass Transfe and keep you posted. Cheers Stoody