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How to get to pitching temperature using ice

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IainM

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So, chilling the last few degrees to get to pitching temperature can be painfully slow, especially if you are brewing in the summer, doing a lager, don't have the time to no-chill, or don't have a counter-flow chiller or brew fridge. Perhaps you just want to get the yeast in there as soon as possible. One way of getting there is to make the wort a little more concentrated, chill part way, and then use ice to bring the brew down to pitching temp. To avoid the risk of infecting your uninoculated wort with cubes from the freezer drawer you can freeze an unopened bottle of water, of known volume (2L, 1L, 750ml, 500ml...), and cut the plastic off and chuck it in when needed. Knowing the volume of water can help you plan your OG. The question is, at what temperature should you add the ice cube in order to exactly hit your pitching temperature? This is actually a very straight forward calculation.

So,
T_pitch is the pitching temperature you want, in Celsius.
T_ice is the temperature of your freezer, in Celsius.
V_ice is the volume of water in the bottle you froze, in litres.
V_bulk is the volume of wort to which you are going to add the ice, in litres.
T_add is the temperature you need to cool down to before putting the ice in, in Celsius.

The equation, then is:


To give an example, image you want to get 18 litres of lager wort at a pitching temperature of 10C, by adding a frozen 2L bottle of water from freezer (at -5C) to 16L of wort of more concentrated wort. In this case Tpitch = 10, Tice = -3, Vbulk = 16 and Vice = 2. Putting these in gives you Tadd = 10 + 0.031 * (6.18 + 41.8 + 333.6) = 21.8. So, you can chill your wort down to 21.8C, put in the 2L of frozen water, give it a stir to melt it, and you end up with 18 litres of wort at 10C, ready to pitch and ferment. I've tried this out a couple of times, and it works very well. In practice, this is all you need to know, but in the next post I'll put a bit of theory for those that might be curious as to why the equation works, and why it is the way it is.
 

IainM

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The previous post was all you need to do this, in this post I'll just explain how I got the above equation. It serves no purpose other than for those who might be interested in it, so please feel free to ignore this post.

The idea is that you start with two things at two different temperatures, the warm wort and the ice, which are then put together and reach equilibrium at the pitching temperature. The key point is that the heat lost from the wort to reach pitching temp (red) is exactly equal to the sum of the heat used to raise the ice to melting point (green), the heat needed to melt the ice (blue), and the heat needed to raise the temperature of the melted ice up to pitching temp (orange).



Here, c_bulk is the specific heat of the wort (4.0 kJ/(kg.K) or so for low gravity worts, up to around 4.1 kJ/(kg.K) for high gravity worts). This is the amount of energy required to increase one kilo of wort by one degree. As a kilo of wort is about a litre, the total energy can be calculated by multiplying it by the volume of wort (V_bulk), and the number of degree difference between the temperature you add the ice and the pitching temperature (delta T_bulk). Similarly, c_ice is the specific heat of ice (2.06 kJ/(kg.K)), so the green bit is the energy for getting the ice from freezer temp to the melting point, and c_water is the specific heat of water (4.18 kJ/(kg.K)), so the orange bit is the energy needed to get the water from melting point to the equilibrium pitching temperature. L_ice->water is the latent heat of melting (333.6 kJ/kg), the amount of heat required to turn 1kg of ice at 0C to 1kg of water at 0C, so the blue part is the energy required to do this. This equation can be rearranged to solve for T_add, and you end up with the formula in the previous post. Voila!
 

Covrich

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Interesting idea.. effectively you maxi biab technique

if you chucked a 2L chunk of ice after cutting the bottle away in say 35ºc wort I wonder how long it would take to actually melt

For those not used to it would have to adjust a few calculations, mash and sparge water and make any water chemistry adjustments..
 

IainM

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Interesting idea.. effectively you maxi biab technique

if you chucked a 2L chunk of ice after cutting the bottle away in say 35ºc wort I wonder how long it would take to actually melt

For those not used to it would have to adjust a few calculations, mash and sparge water and make any water chemistry adjustments..
I tried it to get to lager temp, and it melted pretty quickly, 10 mins or so with the odd stir, and doing it from 35C would be even quicker. You are right, it is a bit like maxi-biab, and the sparge and mash water volume calcs could be done like that.

Actually, now you mention it, you could do a full maxi-biab and only use the ice to chill, all the way from boiling. To calculate the amount of ice you would need, you could use the equation:



So, using the above, you could make 10L of concentrated wort and chuck in 8L of ice (at -3C) at flameout, and you would get 18L of wort at 18C, perfect pitching temp! I'm willing to bet that it would make a quicker cold break that anything you could achieve with a counter-flow chiller to boot.
 

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