# Energy calculation

## Main Question or Discussion Point

Hi there,

As part of my A2 physics coursework, i need to calculate the energy received by a water-antifreeze solution.

Basic setup: Lamp with 40W light bulb at a distance of 5cm away from an aluminium canister, which is filled with 100ml of water-glycol solution (at different concentrations), and time the temperature change of the solution over a period of 15minutes.

I thought that i could simply apply the E=mc(delta)T equation, where i assumed that all the energy supplied by the lamp (36000J over the 15minute period) was received by the solution. I however know that this was not the case, and was wondering what i can do to make my calculations a little more accurate. i.e. i would like to find out approximately what amount of energy is received by the aluminium canister first, and then use that energy as which is received by the water.

I have included the distance from the canister to the lamp, 5cm, incase i can apply some sort of thermal radiation equation?

EDIT: Basically i want the best way to estimate the amount of energy received by the water-antifreeze solution...

Thanks
Joe

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## Answers and Replies

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Mapes
Homework Helper
Gold Member
This is a hard problem. To get anywhere close, you would like to know the irradiance from the bulb as a function of angle, emissivity of the aluminium surface as a function of wavelength, complete geometry (bulb distance, canister size, aluminium thickness), thermal conductivity of aluminium, heat capacity of the solution, and convection coefficient of the surrounding air.

If you must do it by calculation and can't actually run the experiment, perhaps you could make it easier for yourself: assume the 40W is dissipated by a resistor inside the container instead. If the setup can't be changed, I recommend you study a heat transfer textbook that covers conduction, convection, and radiation in detail.

You might want to idealize the container as a flat surface occupying some solid angle from the bulb's viewpoint. Then make an assumption for aluminium emissivity based on whether the surface is rough or smooth. Assume a constant convection coefficient and model the system with the lumped-capacitance approximation when analyzing the transient heating.

Unfortunately i have used the allocated time for my experiment and so cannot further investigate - i actually wished i could now!

The detail you have go into is way past A2 level (A level), but I am sure, that with such poor data gatherings, that with some calculations of some of the terms you have used, i will be able to obtain a decent grade.

"You might want to idealize the container as a flat surface occupying some solid angle from the bulb's viewpoint. Then make an assumption for aluminium emissivity based on whether the surface is rough or smooth. Assume a constant convection coefficient and model the system with the lumped-capacitance approximation when analyzing the transient heating."

Could you please tell me more about this? If you have the time, could you please explain how i can obtain a rough estimate of the energy received by the solution...

The only data gathering i done was of the temperature every 15 seconds, for 15 minutes, at 20%-60% concentrations of antifreeze. I noted that the lamp was 40w, and that it was placed at a fixed distance of 5cm from the aluminium canister (which was painted black) throughout. Im sure i can also measure the thickness of the aluminium, the surface area of the aluminium that was being penetrated by the lamp (as the other half of it that wasnt penetrated was covered with some carpet as insulation), and the size etc.

The only reason i wanted to calculate the energy received by the solution was so i could calculate the specific heat capacity of the solution at every 15 second interval, and put them in a graph to compare.

If you know of any other graph i can plot, other than specific heat capacity vs temperate for each concentration, or any other calculation that you think i can get a decent analysis for, please can you let me know, as i am really stuck in terms of analysing my results, as at the moment it is not at A2 standard.

Sorry if i have waffled on here, but i really just need a good analytical approach to this coursework, and any ideas you may have i will appreciate.

Thanks

Joe

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Mapes
Homework Helper
Gold Member
The problem is that at the beginning, the temperature of each solution will be about the same (the temperature of your lab). After a long time, the temperature will be determined solely by air convection around your container. I can't see the concentration of antifreeze affecting things much except at intermediate times, where there will be some effect (possibly significant, possibly negligible) due to its heat capacity. The confounding effect of all the unknown variables is why heat capacity is not measured this way.

Can your post your temperature data for the different solutions as a function of time? If you can identify some trend that follows the change in concentration in a monotonic way, you might be able to extract a useful conclusion.

I have attached all my physics results, of tables with temperature vs time, and graphs of temp vs time, in microsoft excel format (.xls)

Thanks so much!

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Mapes
Homework Helper
Gold Member
Thanks, johnboy11. I followed your lead in modeling the temperatures as increasing linearly with time, and got the following slopes (°C per sec):

0% 0.00947
20% 0.00779
25% 0.00710
30% 0.00785
35% 0.00744
40% 0.00811
45% 0.00802
50% 0.00824
60% 0.00815

There's really no trend in the data, unfortunately. It looks like the variation in specific heat by varying the solution had a negligible effect on the temperature increase. (If my calculations and interpretation are right.)

All is not lost, however. You have a lot of great data on the temperature increase of an aluminium-and-water (or water-like) system due to incident radiation. You could look up the heat capacity of water and aluminium, and use the temperature data to find out how much energy they absorbed. It would be interesting to compare that to the power output of the lamp.

Also, it looks like you used three thermocouples and averaged their output. Maybe you could compare the results of the thermocouples and predict whether one is out of calibration, for example. You can usually draw a meaningful conclusion from a nice set of data, even if it's not the conclusion you hoped for.

Good luck!