Calculating Time to Cool a Cup of Water in a Freezer

In summary, to calculate the time it takes for a cup of water to reach 15 degrees in a freezer at -20 degrees, given its initial temperature of 30 degrees, mass of 300g, and surface area of 0.03m2, you can use the formula t = q / (U*A*ΔT) with the overall heat coefficient of 13 KJ/hr m2 °C. This results in a time of approximately 5.85 hours.
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Homework Statement


A cup of water put in a freezer (freezer temperature -20 degrees) how long will it take to reach 15 degrees given that its initial temperature is 30. its mass is 300g and its surface area is 0.03m2. the water specific heat is 1.2 J/g °C..

Assume that the heat transfer occurs only to the air around the cup.. and the overall heat coefficient is 13 KJ/hr m2 °C

Homework Equations


q = mc(T)

The Attempt at a Solution


q = mc(Tf - Ti)
300*1.2*15
q = -5400j

so that’s how much energy is required to cool the cup. which is 5.400 Kj
but given 13 KJ/hr m2 °C .. but when do i use the freezer temperature??
im a bit stuck at this point..

any help would be appreciated thanks.
 
Last edited:
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  • #2


Hi there,

To calculate the time it takes for the water to reach 15 degrees, you can use the formula:

t = q / (U*A*ΔT)

Where:
t = time in hours
q = energy required (in J)
U = overall heat coefficient (in KJ/hr m2 °C)
A = surface area (in m2)
ΔT = change in temperature (in °C)

Plugging in the values from the problem, we get:

t = (-5400 J) / (13 KJ/hr m2 °C * 0.03 m2 * (30-15) °C)
t = 5.85 hours

So it will take approximately 5.85 hours for the water to reach 15 degrees. Hope this helps!
 

Related to Calculating Time to Cool a Cup of Water in a Freezer

1. How do you calculate the time it takes for a cup of water to cool in a freezer?

To calculate the time it takes for a cup of water to cool in a freezer, you will need to know the initial temperature of the water, the temperature of the freezer, and the rate of heat transfer. Then, you can use the formula t = (Tf - Tw) / r, where t is the time in seconds, Tf is the final temperature, Tw is the initial temperature, and r is the rate of heat transfer.

2. What is the rate of heat transfer?

The rate of heat transfer is a measure of how quickly heat is transferred from one object to another. This can be affected by factors such as the temperature difference between the two objects, the material of the objects, and the surface area of contact between them. In the case of a cup of water cooling in a freezer, the rate of heat transfer is affected by the temperature difference between the water and the freezer, as well as the material of the cup and the surface area of the cup in contact with the freezer.

3. Can you speed up the cooling process of a cup of water in a freezer?

Yes, there are a few ways to speed up the cooling process of a cup of water in a freezer. One way is to use a container with a larger surface area, as this will increase the rate of heat transfer. Another way is to use colder water, as this will reduce the temperature difference between the water and the freezer, resulting in a faster cooling time. Additionally, you can use a fan to circulate the cold air in the freezer, which can also speed up the cooling process.

4. Why does the initial temperature of the water matter in calculating the cooling time?

The initial temperature of the water is an important factor in calculating the cooling time because it determines the temperature difference between the water and the freezer. The greater the temperature difference, the faster the heat transfer will occur, resulting in a shorter cooling time. This is why colder water will cool faster than warmer water in a freezer.

5. Is the cooling time of a cup of water in a freezer affected by the type of freezer?

Yes, the type of freezer can affect the cooling time of a cup of water. For example, a chest freezer may have a colder temperature than a refrigerator freezer, resulting in a faster cooling time. Additionally, some freezers may have better insulation, which can also affect the rate of heat transfer and therefore the cooling time. However, the exact impact of the type of freezer may vary and can also depend on other factors such as the size and location of the cup in the freezer.

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