Specific Heat of Wort (A Scientific Approach)

[jimmystewart]

Hi, all. I've been a long time (mostly) lurker here on the forums and I've learned a whole bunch from reading countless threads. I've always wanted to give something back, and I think I have a worthwhile contribution to offer. I brewed a batch of beer yesterday and decided to conduct a little experiment.

Since I don't post frequently most of you don't know me well. As a scientist I firmly believe we should all question where our information comes from, so I offer my credentials: I've been brewing for almost 5 years and I've probably done a little more than 500 gallons of beer, wine, and cider. I'm a non-traditional college student aiming for a bachelors' degree in Chemical Engineering and I've managed straight A's in Intro Chem (lab & lecture), Chem I (lab & lecture), as well as the Calculus series (and Differential Equations!). I don't share this to brag, but hopefully to lend credibility to what you'll read below.

Oh, and I welcome any comments and/or criticism of my procedure and/or results. I'd love to collect feedback and maybe get some better equipment and more supplies and do something more in depth in the future, but I have no idea when I'd have the time and resources to do this again. If anyone would like to replicate the experiment, please post about it here!

I'll try to check back on this periodically and answer any questions that come up.

Without further ado:

Specific Heat of Wort (A Scientific Approach)

Abstract:
This experiment makes use of the law of conservation of energy, also called the first law of thermodynamics, which states that the total energy (in this case in the form of heat) of an isolated system is constant. When mixing hot wort and cold deionized water, the heat lost by the wort matches the heat gained by the deionized water. Using the known specific heat of deionized water along with the masses and temperatures of the individual samples, the specific heat of the wort can be calculated.

Introduction:
This experiment was performed out of curiosity arising from my inability to conveniently locate a consistent, reliable answer to the question “What is the specific heat of wort?” in the vast expanse of the internet. This question arose from a synthesis of two of my greatest interests (science and brewing) and specifically came up during a conversation with my chemistry professor around the time of a final exam which included thermochemistry, enthalpy, and calorimetry. A lighthearted challenge was proposed, and my immediate response was: “Why not?”

Hypothesis:
Before beginning the experiment (based on little more than a hunch) it was anticipated that the specific heat of wort was unlikely to vary more than 3% to 5% from the specific heat of deionized water. Because of the additional density expected from the sugars present in the malt extract used to create the wort, it was anticipated that the specific heat of wort would be higher than that of deionized water. The specific heat of deionized water is 4.18 J/g*C, so it was anticipated that the specific heat of wort would fall somewhere between 4.30 J/g*C and 4.39 J/g*C.

Resources:
The formula q=mc(deltaT) where q=heat transferred in Joules, m=mass in grams, c=specific heat in J/g*C, and deltaT=change in temperature. The specific heat (c) for deionized water is 4.18 J/g*C.

Procedure:
(Preliminary) A concentrated wort was made. In a kettle, one pound of specialty grains was steeped in two gallons of store brand bottled purified water until boiling temperature was reached, then the specialty grains were removed, drained into the kettle, and discarded. Six pounds of dry malt extract was added to the remaining water, which was heated to boiling temperature. This wort was boiled for one hour during which two ounces of hops were added. After water loss to the specialty grains and evaporation during the boil, the volume of this concentrated wort was 1.73 gallons. Samples were taken from this concentrated wort for specific heat testing and one sample was set aside to cool to test specific gravity. The remaining concentrated wort was diluted with store brand purified water to a total volume of 5 gallons. Samples were taken from this diluted wort and reheated for specific heat testing and one sample was set aside to cool to test specific gravity.
(Data collection) When measuring masses, record data accurate to hundredths of a gram. When measuring temperatures, record data accurate to tenths of a degree. Measure and record mass and temperature of an approximately 50 gram sample of chilled deionized water. Measure and record mass and temperature of an approximately 50 gram sample of wort. Combine the two samples in a foam cup calorimeter, then measure and record the temperature of the mixture at equilibrium. Repeat this procedure for a total of three trials for concentrated wort, then repeat for a total of three trials for diluted wort. Cool a sample each of concentrated and diluted wort to 60*F to measure and record specific gravity.

Data:
Specific Heat of Wort (A Scientific Approach)
q=mc(deltaT)
all masses in grams, all temperatures in degrees Celsius
specific heat in J/g*C (specific heat of deionized water = 4.18)

method of calculating was:
m(wort)*c(wort)*[Ti(wort)-Tf] = m(water)*4.18*[Tf-Ti(water)]
{solve for c(wort)}

*(I used underscores to try to preserve the table format here, since it seems the forum software doesn't like me pasting in something copied from a spreadsheet.)

Concentrated Wort -
________mass di___temp di___mass___temp___temp______specific heat
________water_____water____wort___wort____mixture____of wort
Trial 1___55.12_____8.3______52.73___76.4____39.9______3.8
Trial 2___59.32_____8.1______52.27___78.0____38.3______3.6
Trial 3___57.02_____8.4______64.56___73.5____41.7______3.9
_______________average of specific heat from all 3 trials:___3.8

concentrated wort specific gravity: 1.190
* Please see comment in notes!

Diluted Wort -
________mass di___temp di___mass___temp___temp______specific heat
________water_____water____wort___wort____mixture____of wort
Trial 1___59.32_____8.4______63.65___78.6____42.3______3.6
Trial 2___64.78_____8.3______53.64___72.3____34.9______3.6
Trial 3___51.34_____8.4______64.35___67.4____39.0______3.6
_______________average of specific heat from all 3 trials:___3.6

diluted wort specific gravity: 1.061

Conclusions:
The results of this experiment were, quite frankly, a surprise. The specific heat of concentrated wort is 9.1% less than the specific heat of deionized water, and the specific heat of diluted wort is 14% less than the specific heat of deionized water. Not only was the difference three times what was anticipated, but the difference was in the opposite direction from what was anticipated. Upon inspecting the results and contemplating the cause of the difference in specific heat, a possible explanation would be that the sugars and other compounds present in the malt extract act as very good conductors of heat. If this were the case, then one might expect the specific heat of concentrated wort to be lower than the specific heat of diluted wort, yet this is contrary to what was found. Granted, the difference between the specific heat of concentrated and diluted wort is only about 5%, but it is measurable difference.

Notes:
In reference to the concentrated wort specific gravity listed on the data page, when this measurement was attempted it was quite literally off the scale of the hydrometer used. By inspecting the scale of the hydrometer and extrapolating the scale beyond the markings provided, the reasonable estimate of 1.190 was deduced. I felt it relevant to include the specific gravities because this is a measurement frequently used by brewers and would make for a convenient reference point when comparing the concentrated wort to the diluted wort.
Lastly, I do want to acknowledge that the type of specialty grains used as well as the type of dry malt extract and variety of hops used were omitted intentionally. The reason for omission was to keep this experiment and any discussion of this experiment focused strictly on the difference between the specific heat of wort and specific heat of distilled water and to avoid discussing opinions of my recipe. Additionally, I acknowledge that these variables could very well affect the specific heat of the wort, and may come into play in a future experiment, but that was simply beyond the scope of what I had the resources to test at the time of this experiment.

Thanks for taking the time to read this, I really enjoyed putting it together!

 

[schematix]

Looks like your numbers are in the ballpark from experiments done a hundred years ago:

http://books.google.com/books?id=9x...XI9ibCh8Yum4u9UF7hOA&ci=66,730,425,545&edge=0

 

[ajdelange]

Well thank you for putting it together. I'm delighted to see others here with an inclination to experiment. As I helped the guy who put together ProMash way back when with calculations involving mixing I must have had some inclination as to what the specific heat of wort and water were. I remember I made him take the variations of specific heat of water with temperature into account which didn't make him too happy but he did it. Anyway I have no recall as to what we did about wort.

In any case your result did at first seem counter intuitive but with a little thought it is clear why the specific heat of wort might be lower than of water. Water forms lots and lots of hydrogen bonds to other water molecules. When you put energy into water a fair amount of it goes into setting those bonds vibrating. That energy does not go into translational motion of the water molecules and thus temperature does not rise so much for a given heat input as it does with other substances. It is, of course, these hydrogen bonds which give water many of its unique prperties and such a valuable heat transfer/storage medium.

Anyway I thought I'd check out your result as it seems you had fun so I made a 'bomb calorimeter' from a Gevalia coffee carafe, two 580 Ω resistors, a power supply and a thermocouple. First I measured out 500 mL (499.1g) of RO (TDS 3 ppm) into the 'calorimeter', cranked the power supply up to deliver 2.076 W and wrote down temperatures over the course of about half an hour. Based on the power input it is easy to plot °C vs joules delivered and use a curve fitting routine to determine the slope and its standard error based on the assumption that the standard error of the temperature measurements was 0.1 °C. Thermocouples just aren't that great but they should be at least linear. For the 499.1 grams of RO water I found a slope of 2003.28 ± 65 J/K (a K is the same size as a °C). The slope for 499.1 g pure water is The slope for 499.1 g of water is 4.181*499.1 = 2086.7 J/K. This is 4.1% more than we supplied so COLD FUSION IS PROVEN!!!. Those who would like to become wealthy beyond their wildest dreams of avarice should PM me for wiring instructions for my Nigerian bank account to which they should transmit their life savings.

Actually it is, of course, temperature measurement error that leads to this result. Adding 1.28 times the standard deviation of the slope estimate gets us to equality in the amount of power required for the water and the amount delivered. This assumes that the power supply readings (checked with a separate Fluke meter) are accurate. It also assumes that the thermal mass of the thermos is insignificant compared to the thermal mass of the water (a fair assumption). Making this assumption, and the assumption that no significant amount of heat is flowing out of the bottle (we'll come back to that) our estimate for Cp is

Cp = (2003.28 ± 65)/499.1 = 4.01378 ±0.130234

Given that the actual value is 4.181 we are off by 4% but the true value lies within a little more than one standard error.

To make 'wort' we made a 12 °P sucrose solution by adding 68.1 gram sucrose to the carafe and collected the same data on this solution. Plotting this data against total joule we get slope 0.00041993 ± 4.34e-06 K/J (again assuming standard error in the temperature measurement of 0.1 K) and the reciprocal of this is 2381.35 ± 24.61 J/K. The estimate of Cv for this solution is

Cp = (2381.35 ± 24.61)/(499.1 + 68.1) = 4.1984 ± 0.04

Not very pleased with the first result for water we repeated the experiment with a couple more resistors in the circuit such that the power supply delivered 6.382 W (Fluke). The idea was to get a wider temperature span and thus drive down the significance of thermometer precision (0.1 °C) and possible error. I also wanted to arrange things so that the temperatures in the 'calorimeter' straddled the ambient temperature. This minimizes any heat gained or lost through its walls. The attached graph shows this data which yields the much more pleasing result that water's Cp is 4.255 (it is actually 4.181 at 25 °C and 4.179 at 30). The slope of the graph is 2123.65 ± 9.88 the slope for 499.1 g of water with an average Cp of 4.180 is 2086 meaning that 37 J/K went to heat the bottle. This is very small (as we had formerly assumed) but if we wanted to deduct it from the heat in the sucrose solution analysis we would have

Cp = (2381.35 - 37 ± 24.61)/(499.1 + 68.1) = 4.1322 ± 0.04

as our estimate for the 12 °P solution. This is, while slightly less than the Cp of water, not statistically so given our error analysis. Based on my experiments (and I'm not claiming anything for them other than what you see here) the null hypothesis would have to be accepted: Wort of 12 ° strength has the same Cp as water.

I went through all of this to have a little fun in the lab this afternoon and posted all this stuff in order to expose you to some of the lab and data manipulation techniques a brewing scientist (one of which I am not, BTW) might use in exploring some of the stuff we worry about. Maybe we did just use water values in ProMash.

 

[doug293cz]

Did you run controls of mixing water with water and wort with wort to get some idea of extraneous heat loss during transfer and from the "calorimeter"?

Edit: Question is for the OP.
Brew on

 

[jimmystewart]

schematix:
Please post your source (Title, Author, etc) as I'd really like to look further into it. I am not entirely clear on the units that author used for specific heat and I'd like to understand how it relates to my experiment. Also, although I'm encouraged that you suggest my results agree, I have found a possible flaw in my experiment (more about that below) and I'd like to figure out how even though I have a flaw, my results seem to agree. Thanks in advance.

ajdelange:
Wow. Your knowledge of electrical circuitry and access to hardware & software seems to exceed my own. An internet high-five to you for your awesome experiment! If I'm reading it correctly, you seem to prove that the specific heat of a 12*plato sucrose solution is nearly the same as the specific heat of deionized water. Twelve degrees plato should correspond to a specific gravity of 1.048, so your experiment seems to correspond more to the second portion of mine. Aside from my possible flaw explained below, could it be that the differences between our findings indicate that the variance of the specific heat of wort vs. the specific heat of water are less dependent on the properties of the sugars, but rather more dependent on other dissolved solids present in wort?
Additionally, you make a very good point about the hydrogen bonds present in water. (Intermolecular forces are given a fair amount of attention in Chem I.) I would suspect that hydrogen bonds would be present in the wort solution based on the likelihood of molecules containing hydrogen bonded to oxygen, or even possibly hydrogen bonded to nitrogen. (I think it's unlikely that we have much fluorine in any of our wort.) Although I'm sure hydrogen bonds are present in wort in an amount capable of affecting specific heat, I would doubt they would be as significant of a factor as in pure water. In short, I agree with you here.
As for your impromptu "bomb" style calorimeter, I think this is probably where your experiment really outdid mine. I was using a foam cup calorimeter with a foam lid, which although suitable for illustrating properties of specific heat in the context of an introductory chemistry lab class, does allow for enough heat loss to surroundings to affect the results of the experiment. (And, thus, the flaw I found.)

doug293cz:
A perfectly valid criticism. In fact, I'm kind of embarrassed that I hadn't thought of this to begin with. Fortunately, I had some deionized water remaining from the gallon I collected for the original experiment, as well as access to the same electronic balance and thermometer from the original experiment. I did three trials today using only the deionized water. Unfortunately, it was no longer possible to perform control trials using wort.

Here are the results from the "control" experiment, in a slightly different format that hopefully will make them easier to read:

all mass in grams
all temperatures in *C
specific heat in J/g*c

Trial 1
mass cold water: 58.55
temp cold water: 4.5
mass hot water: 50.89
temp hot water: 88.6
equilibrium temp: 42.5
Trial 2
mass cold water: 62.11
temp cold water: 4.9
mass hot water: 53.39
temp hot water: 82.5
equilibrium temp: 40.0
Trial 3
mass cold water: 54.54
temp cold water: 5.3
mass hot water: 52.53
temp hot water: 75.6
equilibrium temp: 39.3

Assigning 4.18J/g*C as the specific heat for the cold water and calculating for the hot water, I come up with the specific heat for the hot water to be...
Trial 1: 4.0
Trial 2: 4.0
Trial 3: 4.1
Avg: 4.0

Assigning 4.18J/g*C as the specific heat for the hot water and calculating for the cold water, I come up with the specific heat for the cold water to be...
Trial 1: 4.4
Trial 2: 4.4
Trial 3: 4.3
Avg: 4.3

And, now, I think it's likely that I have a flaw somewhere. Ideally the calculated specific heat rounded for significant figures should have come out to 4.2. I'm fairly confident that the error was introduced into my experiment when vapor (and of course some heat energy) escaped from the hot samples when transferring into the calorimeter. Sure, the density of cold water being higher than the density of hot water would no doubt affect specific heat, and ajdelange mentions that specific heat is temperature dependent, but I wouldn't think it would vary by that much. Maybe he can weigh in on this?

If we compare the results of 4.0 and 4.3 to the value of 4.2 that should have been calculated, we could assume my results are off by approximately +- .15. Frankly, I'll admit that I think this is unacceptable for what I'm trying to demonstrate.

How to fix this? Perhaps instead of using hot samples closer to 100*C, the 'hot' samples should begin around 50*C, to decrease the amount of vapor (and heat energy) lost to the environment?

Thanks, and please keep the feedback coming!

 

[ajdelange]

schematix:
Please post your source (Title, Author, etc) as I'd really like to look further into it. I am not entirely clear on the units that author used for specific heat and I'd like to understand how it relates to my experiment.

In days of yore specific heat was given either in calories per gram-kelvin or BTU per pound- °F. These units of heat were conveniently chosen to make the specific heat of water 1 cal/g-K or 1 BTU/lb=°F. Thus the numbers in the table are relative to pure water. A 12 Bx solution is listed at 0.916 and 0.916*4.181 = 3.83. The correct (in j/g-K) is 3.85. You can get Cp data for sucrose solutions of any strength and temperature at http://sugartech.co.za/heatcapacity/index.php. I think that the sucrose solution will be a fine model for wort.

Also, although I'm encouraged that you suggest my results agree, I have found a possible flaw in my experiment (more about that below) and I'd like to figure out how even though I have a flaw, my results seem to agree. Thanks in advance.

They don't actually agree too well but this is to be expected for reasons I'll get to later. 1.190 is about 42 Bx and the Cp of a sucrose solution of that strength is 3.02. A sucrose solution of strength 1.061 is about 15 Bx and has Cp = 3.77.

Wow. Your knowledge of electrical circuitry and access to hardware & software seems to exceed my own.

The circuit is a resistor connected to a power supply. Not exactly an iPhone 7. Yes, I have a couple of multimeters that let me measure voltage and current and an digital thermometer that lets me read a pair of thermocouples but this is hardly unusual for a geezer of my tooth length. The software I use for all analysis is IGOR (Wave Metrics). It is just incredibly powerful for analysis of this sort. Runs on Mac and PC but I think the youngsters in school these days tend to be exposed to Matlab which will certainly do everything IGOR does and more.

If I'm reading it correctly, you seem to prove that the specific heat of a 12*plato sucrose solution is nearly the same as the specific heat of deionized water. Twelve degrees plato should correspond to a specific gravity of 1.048, so your experiment seems to correspond more to the second portion of mine. Aside from my possible flaw explained below, could it be that the differences between our findings indicate that the variance of the specific heat of wort vs. the specific heat of water are less dependent on the properties of the sugars, but rather more dependent on other dissolved solids present in wort?

You have to read what I wrote very carefully. I said that the conclusion that I would have to draw from my experiment is that 12 °P wort don't have significantly different estimated Cp's based on my data. However, and this is what I want you to take away, in any new experimental procedure you will screw up or if not that do things in a way that is way less than ideal. As you look at your data and your procedure you have to say "Why doesn't my Cp ~ 4 for a 12 °P solution match what's in the textbooks?" To answer that question you look at the final calculation Cp = (∂E/∂T)/mass (E is energy supplied) which makes it clear that you have an error in you energy measurement, your temperature measurement or your mass measurement. You then go on to explore each of those measurements and see what you can do to drive the error down. You, I believe, and I both are assuming that all the heat we add is going where we think it is. It isn't. Some escapes to the ambient (if the experiment is at any temperature other than the ambient) and of what's left not all goes to the water - some goes to warm the calorimeter whatever it is. The calculation is very sensitive to this. I calculated about 4 for Cp when the answer is 3.85. That's only a 5% difference. If I'm off by 5% in my heat calculation then little surprise that I'll be off in my Cp estimate by that much.

With my 'apparatus' further investigation revealed that I lose about 83 mW through the walls of the 'calorimeter' for each °C difference between water temperature and ambient. The thermal mass of the half liter of water I use is 2086 J/K but the thermal mass of the 'calorimeter' is 102 J/K. That's about 5%. To discover this I needed to make much better measurements than I did on water and use its known Cp to 'calibrate' the calorimeter i.e. find it's thermal mass. To give you an idea of how nit-picky one has to get I noticed that as the experiment progressed (temperature in the 'bomb' goes up) the current dropped from 400 to 388 ma. All good engineers know that resistance goes up with temperature and so it was a simple matter to incorporate the temperature into the delivered power calculation. I won't go into more details as I think the resistor thing make the point that you need to understand the process thoroughly and (this is the part we all hated in school) you must do a thorough error analysis. Having done this and taking these factors into account I am able to estimate 12 °P sucrose solution at 25 °C as having estimated Cp of 3.849 ± 0.01 joules/K·g. The Sugar Engineers (site I referenced earlier) say the correct answer is 3.85 so I am, of course, delighted at what you can do with 'kitchen chemistry' but am also fully aware that it is possible to get the right answer with the wrong technique.

Additionally, you make a very good point about the hydrogen bonds present in water. (Intermolecular forces are given a fair amount of attention in Chem I.) I would suspect that hydrogen bonds would be present in the wort solution based on the likelihood of molecules containing hydrogen bonded to oxygen, or even possibly hydrogen bonded to nitrogen.

Yes, there are lots of hydrogen bonds in wort - between the water molecules of which it is mostly made up. As you decrease the mole fraction of water molecules by adding sugar molecules (which don't hydrogen bond to each other) you decrease the relative number of hydrogen bonds and so Cp goes down the more sugar you have.

As for your impromptu "bomb" style calorimeter, I think this is probably where your experiment really outdid mine. I was using a foam cup calorimeter with a foam lid, which although suitable for illustrating properties of specific heat in the context of an introductory chemistry lab class, does allow for enough heat loss to surroundings to affect the results of the experiment. (And, thus, the flaw I found.)

Another point I really want to emphasize is that while my calorimeter may indeed have it all over yours I still had to be scrupulous in my characterization of it in order to get the correct answer. This involved measuring its thermal mass AND its heat loss to the ambient. If you are to get good answers you will have to do the same.