Physics question

[MrNate]

I know I should be able to figure this out, but for some reason I'm stumped.

How long would it take a 1500w electric heating element to bring 15 gallons of 60f water to a boil? How about a 4500w?

Better yet, what's the formula?

[Jeff]

Formula I can give, a couple numbers I will have to fill in later:

Power = (Mass)(Specific Heat)(Change in Temperature)

That will get you to boiling temp, it takes another formula for the phase change. I think it is:

Power = (Mass)(Enthalpy Change from water to vapor)

Using water will probably be a pretty close estimation.

[MrNate]

That's great!

Just 2 questions:
1. is Specific Heat a known constant?
2. How do I get time from Power?

Thanks for the help!

[Jeff]

Again if I am remembering correctly specific heat is a constant under the temperature ranges and pressures we are exploring.

Power is a function of time. Watts can be converted to BTU/min.

1 W = 0.05687 Btu/min.

Based on a couple quick calcs, to raise the temp of wort from 60*F to 212*F would take 212 Minutes at 1500W and 72 minutes at 4500W. Does this sound close to anybody?

[MrNate]

Jeff,

I'm still a little fuzzy on the specific heat, but I think I understand roughly what you're getting at. Can you take a look at this spreadsheet and let me know if it seems at least roughly accurate? I basically solved for BTUs and used the BTU-min/watts conversion you supplied and came pretty close to your numbers.

Based on this, it seems like I can get away with using a 2000w (120v) heating element on my 5-gal portable system, but I'll need to step up to 220v when I build my basement brewery.

Thanks!

[darylM]

Originally posted by Jeff

Based on a couple quick calcs, to raise the temp of wort from 60*F to 212*F would take 212 Minutes at 1500W and 72 minutes at 4500W. Does this sound close to anybody?

If you are close, I believe my next heating element will be powered by propane.

[Jeff]

The spreadsheet looks good. It looks like the numbers should work.

[MrNate]

Awesome, thanks Jeff!