Calculating the Time to Form an Ice Sheet 25 cm Thick

In summary, to calculate the time it will take to form a 25 cm thick ice sheet, you will need to know the thermal conductivity, area of the sheet, and heat of fusion of water. Using these values, you can use the equation (change in time) = Q/(H*A*(change in temp.)/thickness) to find the time. The thermal conductivity of ice is typically around 2.2 W/mK and the heat of fusion of water is 334 kJ/kg. The answer will be in units of time (minutes, hours, days, etc).
  • #1
gizzard
4
0
Hello,
Can someone help me with this problem:

An ice sheet forms on a lake. The air above the sheet is -15 degrees C and the water is 0 degrees C. Assume that the heat of fusion of water freezing on the lower surface is conducted through the sheet to the air above. How much time will it take to form a sheet of ice 25 cm thick?


I believe that I can "legally" convert cm of water to grams of water. Therefore 25 grams.

I assume that I

will find time through the eqn: (change in time) = Q/H.

and find H through the eqn: H kA(change in temp.)/(thickness)

and find Q through the eqn: (heat of fusion)(mass)
 
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  • #2
My problem is that I don't know what values to put into the equation. The answer should be in units of time (minutes, hours, days, etc). Any help would be appreciated. Thank you!To calculate the time it will take to form a sheet of ice 25 cm thick, you will need to know the thermal conductivity (k) of the ice sheet, the area of the sheet (A), and the heat of fusion of water (Q). Using these values, you can calculate the time it will take to form the ice sheet using the equation: (change in time) = Q/(H*A*(change in temp.)/thickness). In this case, the change in temperature is -15 degrees C, and the thickness is 25 cm. The thermal conductivity of ice can vary depending on different factors such as purity, temperature, and other additives, but for the purposes of this calculation you can use a value of 2.2 W/mK. The area of the sheet is not provided, so you will need to calculate that. Finally, the heat of fusion of water is 334 kJ/kg. Once you have all of the necessary values, you can plug them into the equation and solve for the amount of time it will take to form a 25 cm thick ice sheet. The answer will be in units of time (minutes, hours, days, etc).
 

1. What is the definition of Thermodynamics?

Thermodynamics is a branch of physics that deals with the relationship between heat, energy, and work, and how they affect the behavior of matter.

2. What is the first law of Thermodynamics?

The first law of Thermodynamics, also known as the Law of Conservation of Energy, states that energy cannot be created or destroyed, only transferred or converted from one form to another.

3. What is the second law of Thermodynamics?

The second law of Thermodynamics states that in any energy conversion or transfer, some energy will always be lost in the form of heat. This means that the total entropy, or disorder, of a closed system will always increase over time.

4. What is an example of a problem in Thermodynamics?

An example of a problem in Thermodynamics could be calculating the efficiency of a heat engine, which is a device that converts thermal energy into mechanical work. This involves analyzing the energy input, output, and losses in the system.

5. How is Thermodynamics used in real life?

Thermodynamics is used in many real-life applications, such as power plants, refrigeration systems, and engines. It is also important in understanding the behavior of gases, liquids, and solids, and is essential in the design and optimization of various industrial processes.

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