[NarrowPlant20]

Hi people!

Basically I have to find out how to calculate the time it takes for -20 degree celsius pure ethanol (27.27 liters) to cool down to -40 degrees celsius in a cooler (which sits on -40). I also have to find out how long it takes to do the same for ethanol at -5 degrees (though I assume its the same application as the other question).

If someone could show me how to go about doing this first question, that would be fantastic. I have been looking around online but can't seem to find anything both when I search specifically and more generally.

Thank you very much for your time in advance!

[Borek]

This is quite difficult, as the exact answer depends on the geometry of the vessel and many other parameters.

In practice this kind of problems is often easier to solve experimentally.

Also, technically the answer is "it will never cool down to -40", as the temperature of the cooled down converges to the temperature of the surroundings, never getting there. It doesn't matter practically (you can always say everything below 39 is close enough), still it changes how the problem should be defined/question asked.

There are some approximate methods to estimate such time, but you would nee to find an engineer using them in practice, as far as I am aware none of the regulars works with this type of problems. I can be wrong though.

[Corribus]

Approached theoretically you have to solve the heat equation. You would need at a minimum information about the geometry and size of the container, plus (temperature-dependent) heat capacity/conductivity data for ethanol and the environment. And some skill in solving differential equations. Your container material will also likely impact the heat transfer, so you would likely need to incorporate that into your modeling, and the degree of mixing will also impact your boundary conditions.

This is all doable in theory but not easy. As borek suggested, easier to just get a thermometer and a clock and measure the temperature over time, unless you need to build a flexible model (e.g., for process optimization). In that case, find a chemical engineer.

[NarrowPlant20]

Thank you all very much for your input - no wonder I couldn't find something like this just lying around on Google! I believe I will go for the heat equation approach, with a couple of the questions, then the practical approach and see if I can't find a solid pattern to work off of (same containers!).

Thank you so much you saved my skin 

[Enthalpy]

I will go for the heat equation approach

Understand the previous answers as strong understatements. Predictions based on computations are unreasonable, unless you're happy with /*5 uncertainty.

Already the initial amount of turbulence in the liquid changes the result.