In HBD #1206, Andy Phillips asks about the heat capacity of crushed malt, to be used for calculations of infusion mashes. I have found that the number 1350 (where water is about 4200) to work well for me. I believe the units re J/Kg/K, but this is not important. Alternately, one could use the dimensionless number 0.32 for the malt, where water is equal to one. Of course, this will vary somewhat depending on the type of malt used, the moisture content of the malt, etc. but this should be a good starting point.
For those not familiar with these calculations, I will present them here:
First, let
Cpm= heat capacity of your malt, about 0.32 Cpw= heat capacity of water, 1.0 Mw = mass of water used Mm = mass of malt used Tw = temperature of strike water Tm = beginning temperature of malt (usually room temperature) Tf = final temperature of mixture (rest temp)Masses and temperatures can be in any units, as long as you are consistent.
The basic formula, then, is
(1) Tf = (Cpm*Mm*Tm + Cpw*Mw*Tw)/(Cpm*Mm+Cpw*Mw)This can be rearranged in many ways to solve for the desired unknown. For example, if we want to know the quantity of water to add to result in a desired protein rest temperature, we can write
(2) Mw = Cpm*Mm*(Tf-Tm)/(Cpw*(Tw-Tf)) or, using the numbers for Cpm&Cpw, (3) Mw = .32*Mm*(Tf-Tm)/(Tw-Tf)SO, suppose you have 4Kg of malt at 25C, and you want to add some quantity of water at 54C to achieve a protein rest temperature of 50C:
Mw = .32*4*(50-25)/(54-50) = 8Kg of waterThese formulas can also be used to calculate additional water quantities to raise the mash temp further. However, different variables must be used: Instead of Mm, we will substitute Mmash, the mass of the mash, equal to the total mass of malt and water used so far; for Tm, we will substitute Tmash; and for Cpm, we must use Cpmash, calculated as
Cpmash = (Cpm*Mm +Cpw*Mw)/(Mm+Mw) Thus, the revised formula (2) is Mw = Cpmash*Mmash*(Tf-Tmash)/(Tw-Tf)continuing our example, we have Mmash = 4Kg +8Kg = 12Kg, Cpmash = (.32*4+1*8)/(4+8)= .773. Suppose our mash temp is still at 50C, and we want to raise it to 66C for a sacharification rest using some quantity of water at 100C. Then
Mw = .773*12*(66-50)/(100-50) = 3Kg of additional (boiling) water.Some simplifying assumptions have been made here, but they seem to work out just fine. (So please don't get on my case about enthalpies of mixing, non-additive Cp's, etc.) You may need to play around with the value of Cpm to get these equations to work out better for you. Also remember that your mash tun will absorb some heat, resulting in a rest temperature slightly lower than that predicted here. You may want to shoot for a degree or so higher to compensate. Note that your boiling water temp may not be 100C. Equation (1) may be rearranged, if instead it is desired to know, for example, what water temperature should be used to obtain a given temperature rest for a given volume of water (if one is shooting for some specific mash thickness).
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