Picnic ice chest

sonhouse
Posers and Puzzles 07 Jul '06 06:58
1. sonhouse
Fast and Curious
07 Jul '06 06:581 edit
So you have an ice chest for your picnic and its 0.5 meter ^3. (1/8 cubic meter). So the problem is this: You can fill it completely with ice which at zero degrees C has X amount of cooling power, heat absorbtion, whatever you want to call it, and its easy to see if its completely full of ice you have no room for food but if its empty you have plenty of room for food, 100 of the volume but no cooling power. So what kind of formula could you conjure up to calculate the most cooling power for the buck balanced with the most food volume?
Say its filled halfway, then you have X/2 cooling and Y/2 volume for food but is that the best that can be done? You want to keep the food at 7 deg C or less for 24 hours and the food starts out at 12 deg C.
The insulation is R12, So what is the maximum amount of food you can put in the box with the minumum amount of ice? You can assume the food to be the same density and heat capacity as water.
2. 07 Jul '06 11:551 edit
Originally posted by sonhouse
So you have an ice chest for your picnic and its 0.5 meter ^3. (1/8 cubic meter). So the problem is this: You can fill it completely with ice which at zero degrees C has X amount of cooling power, heat absorbtion, whatever you want to call it, and its easy to see if its completely full of ice you have no room for food but if its empty you have plenty of roo ...[text shortened]... numum amount of ice? You can assume the food to be the same density and heat capacity as water.
You've neglected to tell us the ambient conditions. If I were at the North Pole I doubt I'd need any ice in the box; I'd be surrounded by the freezing stuff. Do you want a function of outside temperature? Does this picnic take place in the shade of a tree or in direct sunlight?

And what does "R12" mean?

Also if the food starts of at 12 deg C, how quickly do you need to get it to 7 before it goes off? Is the food something like strawberries with a high surface area to mass ratio or more like watermelon (low)?

EDIT
Just Googled for R12 - according to Home Depot it's equivelent to 2" of Polyurethene/Polyisocyanurate
3. sonhouse
Fast and Curious
07 Jul '06 15:17
Originally posted by howardbradley
You've neglected to tell us the ambient conditions. If I were at the North Pole I doubt I'd need any ice in the box; I'd be surrounded by the freezing stuff. Do you want a function of outside temperature? Does this picnic take place in the shade of a tree or in direct sunlight?

And what does "R12" mean?

Also if the food starts of at 12 deg C, ...[text shortened]... for R12 - according to Home Depot it's equivelent to 2" of Polyurethene/Polyisocyanurate
Sorry, ambient I just assumed at 20 C. I think you can discount surface area or just treat them as equal, for instance orange juice, mostly water comes in rectangular containers, low surface area but like you say strawberries are like fjords!