The general formula for cooling requirements is:
Q = M x Cp x ΔT
Where Q is the heat required in (kilo)joules M is the mass in kilograms, Cp the specific heat of beer in (kilo)joules/kilogram-kelvin and ΔT is the change in temperature in kelvin. In practice, you can do the temperatures in celsius and the mathematics is the same. And it doesn’t matter if you give the specific heat, Cp, in kilojoules or joules as long as you do the heat Q consistently. The specific heat of beer is 4.05 kilojoules/kilogram kelvin
For example, if you have some cans of beer that you want to cool down in the fridge, you multiply the mass of beer in kilograms by 4.05 and by the temperature drop in celsius and that gives you the amount of heat to be removed by your fridge.
This is the formula you use when determining the power requirement for a cooling system for crash cooling beer in fermenters after the fermentation is finished.
Another formula is used to express the heat created through fermentation, which is an exothermic process. It is ultimately glucose that is consumed in fermentation as maltose is broken down into glucose by the yeast first. The amount of heat produced in the reaction(s) that convert(s) glucose into ethanol and further yeast metabolism has been estimated at 219 kilojoules per mole, which is 1.217kJ/gram (Briggs et al. Brewing Science and Practice, 2004, section 14.2.3). We need to estimate the quantity of glucose to be fermented.
Volume of wort in litres (V)
Specific gravity 20/4 of wort (or the density of wort which is numerically the same).
degrees Plato of wort
Estimated percentage of fermentable extract % —not all the extract is fermentable. Dextrines, proteins, beta-glucans etc are not fermentable by most yeasts. Briggs et al use the value 75% for an average fermentability of wort. Kunze and Narziß estimate closer to two thirds fermentability during primary fermentation.
Fermentable Extract (kg) = Plato/100 x Volume x Specific gravity 20/4 x fermentability%
Q = Fermentable Extract (kg) x 1217 (kJ/kg).
This estimate is actually twice as much as Kunze and Narziß provide.
Narziß states (Abriss der Bierbrauerei,7/e 2005, p.219f) that fermentation produces 570kJ/kg glucose fermented and recommends 780kJ cooling capacity per hectolitre fermenting wort per day, with a peak demand requirement of 2.5 kg extract per hectolitre per day 1465kJ). Cooling surface area should be 2 to 2.5 meters squared per 100 hl. Narziß puts the cooling requirements of ales at 1880kJ/hl day with a peak demand of 4.5kg extract. Cooling fluid shouldn’t ever be cooler than -4˚C to prevent beer freezing on the sides.
Kunze’s numbers agree with Narziß.