Dry ice sublimation, heat balance

AI Thread Summary
The discussion focuses on determining the optimal amount of dry ice needed to keep 40 kg of frozen pizza dough at -18°C during a three-day transport at 20°C. Key calculations involve the specific heat of dry ice and the dough, as well as the heat of sublimation of dry ice. The heat flow from the environment into the Styrofoam pack is also considered, with the thermal conductivity of Styrofoam factored into the calculations. The user has provided an Excel file with detailed calculations but seeks confirmation on the accuracy of their results. Overall, the aim is to ensure that the dough remains at the desired temperature throughout the transportation period.
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Homework Statement


The problem is this:
what is the optimum amount of dry ice inside the Styrofoam pack, if we want to received a frozen dough (temp.-18) after 3 days of transportation in temperature 20 C ?
My calculations and data placed in the attached excel file, but I'm not sure if they are correct.
Below I present my reasoning :
1. Initial temperature of the dough is -18 C deg. The dough is frozen to temp. -78 C. degrees by placing inside the Styrofoam pack with dry ice.
2. From the (Measuring the Heat of Sublimation of Dry Ice with a Polystyrene Foam Cup Calorimeter, Albert W. Burgstahler and Clark E. Bricker, 1991)
-- specific heat of dry ice is: 0.805 J/g*C
-- heat of sublimation of dry ice is: 580 J/g
and internet sources:
-- specific heat of the dough is 2.7 J/g*C
the energy equivalent in dry ice sublimation process from the second point corresponds to about 48 kg of dry ice (?, cell G11 in excel) ?
I understand that this amount sublimate and by the time of transportation of the product. It will "take" energy from product lowering its temperature.
3. When transporting in +20 C deg. outdoor temp. Heat energy will flow from the environment to the interior of the box by increasing the temperature of the product.
How much of dry ice we need to ensure product will have exactly -18 C after traveling 3 days in the Styrofoam pack in temperature +20 C deg ?

Homework Equations


581f2a250b1c453b5ce1ab7130d5f3c2.png

q - heat flowing through the object
λ - thermal conductivity (for styrofoam: 0.036)
S - area through which the heat flows (3,66 m^2)
t - time of transportation (259200 sec)
delta T - difference of temperatures (98C = -78C to +20C)
d - styrofoam thickness (0.12m)

See excel file

The Attempt at a Solution



See excel file[/B]
 

Attachments

Physics news on Phys.org
You never state how much dough you are trying to keep cool. Quantity makes a difference in the final result. :wink:
 
@ SteamKing. Thank you for remark. Dough quantity is 40 kg - balls of diagonal 4 cm, 30 gr each. So 1333 balls, 30 gr each, 4cm diagonal, made of pizza dough.
I put the data into new attachment below.
 

Attachments

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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Thread 'Variable mass system : water sprayed into a moving container'

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