How long would it take to cook twice the amount of beans?

[kaleidoscope]

I was reading this article from the exploratorium museum about how longer it would take to cook a twice as big turkey. According to geometric scaling it would take 2*1.26/1.59 = 1.59 times longer, derived from here:

If I double the weight of the turkey:
The volume, a three-dimensional quantity, gets bigger by a factor of
2**3/3 = 2.00

The surface area, a two-dimensional quantity, gets bigger by a factor of
2**2/3 = 1.59

The distance to the center, a one-dimensional quantity, gets bigger by a factor of
2**1/3 = 1.26

I was wondering if the same would apply when cooking a pot of beans or if we should take into account each individual bean surface instead (which would leave the surface area factor at 2, then cancel the volume factor, and leave the cooking time factor at 1.26x)

 

[Borek]

I was wondering if the same would apply when cooking a pot of beans or if we should take into account each individual bean surface instead (which would leave the surface area factor at 2, then cancel the volume factor, and leave the cooking time factor at 1.26x)

I have a pot of beans that I know need - say - 1.5 hours cooking. I take same amount of beans, I put them in separate pot, and I cook them also. Will it take any longer, or will both pots be ready at the same time?

 

[kaleidoscope]

I have a pot of beans that I know need - say - 1.5 hours cooking. I take same amount of beans, I put them in separate pot, and I cook them also. Will it take any longer, or will both pots be ready at the same time?

Ok, it takes 1.5 hours to cook your pot. Now you put twice as many beans in your pot and cook them, how long will it take now?

 

[sophiecentaur]

There is also the factor of the actual power available. It is true that an oven full of stuff often doesn't reach the same temperature, even, as it will with one pot.
This is particularly true when using a microwave oven, which uses most of its power on heating the target food rather than the oven and the room.
I think the '20 minutes per 500g plus 20 minutes' (and don't forget to include the stuffing, which has a lot of water in it) works pretty well and you can't afford to undercut that value by much or your poultry may have a pink inside. So there is a lot of empirical truth in what they say.
The Physics of it just isn't that simple, I fear.

 

[Borek]

This is in a way similar to difference between intensive and extensive properties.

Cooking of beans has two stages - first, you have to bring the pot to boil. Then you have to wait till beans cook. One of the stages requires amount of heat that depends on the amount of water and beans, amount of heat in the other stage doesn't depend on the amount of water and beans. Can you say which is which? Can you say - assuming constant speed of delivering the heat - length of which stage depends on the amount of beans?

 

[LennoxLewis]

This is typically something you want to evaluate numerically, for instance with Comsol Multiphysics. However, the accuracy of your results would still be limited by estimated values of for material properties like the thermal conductivity.