Dry ice sublimation, heat balance

In summary, the problem is to determine the optimum amount of dry ice inside a Styrofoam pack in order to receive a frozen dough with a temperature of -18°C after 3 days of transportation in an environment with a temperature of 20°C. The calculations and data have been placed in an attached excel file, but their accuracy is uncertain. The reasoning behind the solution includes the use of specific heat and heat of sublimation values for dry ice and dough, as well as the thermal conductivity of Styrofoam. The quantity of dough is 40 kg, made up of 1333 balls with a diagonal of 4 cm and a weight of 30 grams each.
  • #1
nooldor
2
0

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

  • Data and solution.xlsx
    9.1 KB · Views: 314
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  • #2
You never state how much dough you are trying to keep cool. Quantity makes a difference in the final result. :wink:
 
  • #3
@ 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

  • Data and solution.xlsx
    9.2 KB · Views: 266

FAQ: Dry ice sublimation, heat balance

1. What is dry ice sublimation?

Dry ice sublimation is the process in which solid carbon dioxide (CO2) directly turns into gas without passing through the liquid state. This is because the atmospheric pressure is not high enough to keep the CO2 in its liquid form.

2. How does dry ice sublimation affect heat balance?

Dry ice sublimation has a cooling effect on its surroundings due to the absorption of heat energy required for the solid to gas phase change. This can disrupt the heat balance in a closed system, causing a decrease in temperature.

3. What factors can affect the rate of dry ice sublimation?

The rate of dry ice sublimation can be affected by factors such as temperature, pressure, surface area, and humidity. Higher temperatures and lower pressures can increase the rate of sublimation, while higher humidity can slow it down.

4. Is dry ice sublimation dangerous?

Dry ice sublimation can be dangerous if handled improperly. The release of large amounts of CO2 gas can lower the oxygen levels in a confined space, leading to suffocation. It can also cause frostbite if touched with bare skin.

5. How can dry ice sublimation be controlled in a laboratory setting?

Dry ice sublimation can be controlled by storing it in a well-ventilated area to prevent the buildup of CO2 gas. It can also be placed in a container with a lid to slow down the sublimation rate. Additionally, using proper protective equipment and handling procedures can ensure safe use in a laboratory setting.

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