Heat Capacity of 'dry' coffee and brew temperature profiles

#1: Post by **trzynkaa** » July 16th, 2009, 11:39 pm

Heat Capacity of 'dry' coffee and brew temperature profiles

Overview:
I've been working out ways to manage the temperature profile on my HX machine and after reading Scott Rao's book (specifically pages 30-31), I've been thinking about the heat capacity of dry coffee and how it will affect the temperature profile in the basket.

Since an HX machine normally provides an "HX hump", I'm interested in learning how I can optimize the hump characteristics to "feed-forward" the temperature of the water/coffee mix in the basket and bring the mix to brew temperature quickly. Ideally, the "feed-forward" should occur completely within the pre-infusion period to take advantage of the built in thermal and hydrodynamic properties of the E61group head. To do this, I will need to know the heat capacity of dry coffee.

I read that Andy Schecter has estimated the heat capacity (Cp) of dry coffee to be 0.4 times that of water. The value of 0.4 times that of water seemed to be rather large to me, so in my boy scientist way, I set out determine the heat capacity of dry coffee.

The lab work:
The commonly listed value for the heat capacity of water (at 25C): Cp = 4.1813 J/(gK)
Andy Schechter's heat capacity of dry coffee converts to Cp = 1.67 J/(gK)

I first tried to determine the heat capacity of coffee using a styrofoam cup. This did not work well. I was confused by the temperature data I collected. It appeared the heat capacity of the styrofoam cup was a significant source of error. Useful results of this experiment were only that I needed a better calorimeter.

Try again using a stainless-steel vacuum insulated thermos bottle and determine the heat capacity of coffee relative to that of water by adding about 20g of about 70 F coffee to about 50g of about 180 F water. First do some control experiments just mixing water at different temperatures to see if the results are close enough attempt to measure the Cp of coffee.

Figure 1 - Experiment 1: Cold water added to hot water.

Experiment 1a:
Predicted temperature:
33.5x163x1+14.2x66.1x1 = 47.7xTx1
6399.12/47.7 = T =134.1 F
Measured temperature = 132.8 F
Temperature error = 132.8-134.1 = -1.3 degrees F

Experiment 1b:
Predicted temperature:
27.5x162.8x1+7.5x66x1 = 35xTx1
4972/35 = T = 142.0
Measured temperature = 137.7 F
Temperature error = 137.7-142.0 = -4.3 degrees F

Figure 2 - Experiment 2: Cold water added to hot water.

Experiment 2a:
Predicted temperature:
44.5x179.2x1+17.5x66.7x1 = 62xTx1
9141.65/62 = T =147.45
Measured temperature = 145.1 F
Temperature error = 145.1-147.45 = -2.35 degrees F

Average temperature error (experiments 1 and 2) = -2.65 +/-1.52 degrees F

These results are better than I expected since I'm simply ignoring heat loss to the environment and heat transfer from the thermos bottle back into the mix after mixing.

Figure 3 - Experiment 3: Cold water added to hot water and cold coffee added to hot water.

Experiment 3a:
Predicted temperature:
52.9x179x1+10.1x69.5x1 = 63xTx1
10171.05/63 = T = 161.45
Measured temperature = 160 F
Error = 160-161.45 = -1.45 degrees F

Average temperature error (experiments 1, 2 and 3a) = -2.35 +/- 1.38 degrees F

I then calculate the Cp of coffee adjusted for the average temperature error from experiments 1,2 and 3a...

Experiment 3b:
54.6x177.5x1+20.1x71xCp = 54.6x166x1+20.1x(166-(2.35+/-1.38))xCp
9691.5+1427.1Cpc = 9063.6+(3289.37+/-27.74) Cp
9691.5-9063.6 = ((3289.37+/-27.74)-1427.1) Cp
627.9/(1862.27+/-27.74) = Cp = 0.337 +/- 0.005 (relative to water)

Figure 4 - Experiment 4: Cold water added to hot water and cold coffee added to hot water.

Experiment 4a:
Predicted temperature:
48.7x180x1+3.8x71x1 = 52.5xTx1
9035.8/52.5 = T = 172.11
Measured temperature = 168.9 F
Error = 168.9-172.11 = -3.21 degrees F

Average temperature error (experiments 1, 2, 3a and 4a) = -2.52 +/- 1.25 degrees F

Calculate the Cp of coffee adjusted for the average temperature error from experiments 1, 2, 3a and 4a...

Experiment 4b:
51x179x1+20x74.3xCp = 51x166.7x1+20x(166.7-(2.52+/-1.25))xCp
9129+1486Cp = 8501.7+(3283.6+/-25)Cp
9129-8501.7 = ((3283.6+/-25)-1486)Cp
627.3/(1797.6+/-25) = Cp = 0.349 +/- 0.005 (relative to water)

The results:
Averaging the values I calculated for the Cp of dry coffee, I get Cp=0.334+/- 0.005 relative to the Cp of water.

I will presume the Cp of water does not vary significantly between 25C and 95C and so in standard units I estimate:

Cp of 'dry' coffee ~= 1.434 +/- 0.021 J/(gK)

Andy Schecter's value of 0.4 times the Cp of water is close to what I'm calculating here. Since dry coffee contains a lot of cellulose fiber, the calculated value for the heat capacity of coffee should be close to that of wood. An internet search reveals that the heat capacity of wood ranges from 1.7 to 2.7 J/(gK) so these numbers are reasonable.

So what does 'dry' coffee mean? How much water does 'dry' coffee contain? I might need to weigh some coffee, bake it dry and weigh it again. Another boy scientist experiment in the making...

So what do you think about this?

#2: Post by **another_jim** » July 17th, 2009, 5:25 pm

You've done a lot of very high quality work here, and it's unfair that you haven't gotten any comments.

I think a problem for readers is that you haven't been clear on the goal. The heat constant of coffee is a constant, so presumably it doesn't not enter as a factor one needs to think about in everyday coffee making. I gather you believe it's important in machine design, and maybe in the invariable fundamentals of barista and coffee prep procedure.

Can you please expand your thoughts on this. For instance, if the heat constant of coffee were double of what you measured, how would machine design and coffee prep procedure change?

#3: Post by **Psyd** » July 17th, 2009, 5:34 pm

another_jim wrote:You've done a lot of very high quality work here, and it's unfair that you haven't gotten any comments.

It is NOT unfair. there are quite a few of us that are still sitting stunned, in front of our monitors, unable to do much else. I think you meant to say untimely. ; >

Truth is that there are a bunch of us that are hobbyists, and are not quite at that level of geekdom. We are, however, close enough that this is interesting to watch, and we tend to wait for the final conclusion after fifteen rounds of counter-charts and contradictory science, paradoxical results and the occasional clipboard flinging rant, scroll to the bottom and see if there is anything that we might alter in our approach to our alter every morning that may appease the Brown Goddess of Awakefullness.
We are, however, still really amazed at this stuff.

#4: Post by **cannonfodder** » July 18th, 2009, 1:22 am

I will agree with both you and Jim. Lots of work in those graphs and some neat stuff but I am still unclear on what your goal is. Having difficulty seeing the trees through the forest. Could you explain a bit more.

#5: Post by **CafSuperCharged** » July 19th, 2009, 2:39 am

That is a very nice experiment Andrew (trzynkaa). We home-barista already should be able to monitor grind quality with an electron microscope and laser device to measure particle distribution - the kit you introduce is relatively simple, so I am not complaining about you raising the bar

.

Based on your results, can you now extrapolate to the heat bump needed initially to heat the coffee in the filter basket? For best results?

If we now reverse engineer the design process these Italian engineers went through e.g. before 1961 when they worked on the E/61 at Faema's? Pre-infusion and pressure ramp-up, over-heated group that the barista flushes to the right amount of overheating in order to have the right temperature bump for the best result. Grinders that produce snowflakes, not just cut the coffee up. Compared to today, their bicycle had no handlebars, but boy did they ride it.

From a physics point of view, I have a validity question that I cannot answer myself. Throwing the coffee in water, with the coffee absorbing the water, surrendering through dilution or osmosis substances to the water, does that constitute a valid experiment to determine coffee Cp?

Regards
Peter