Evaporative cooling of beverage problem involving thermodynamics and heat concepts

In summary, the conversation discusses the possibility of keeping a cold beverage cold on a warm day by slipping it into a porous ceramic container soaked in water. The solution manual calculates the rate of water loss from the container, taking into account the environment and container temperatures, emissivity, and neglecting other energy exchanges. However, it does not consider the transfer of heat needed to bring the water temperature to 100 degrees C.
  • #1
laksate
3
0
A cold beverage can be kep cold even on a warm day if it is slipped into a porous ceramic container that has been soaked in water. Assume that energy lost to evaporation matches the net energy gained via the radiation exchange through the top and side surfaces. The container and beverage have temperatures of 15 degrees C, the environment has temperature of 32 degrees C and the container is a cylinder with radius of 2.2cm and height of 10cm. Approximate the emissivity as 1 and neglect other energy exchanges. At what rate dm/dt is the container losing water mass.

Now I have attached the solution from the solutions manual. However my problem with the solution is shouldn't it be considered that heat must be transferred to bring the temperature of the water up to 100 degrees C?
 

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  • #2


can you guys access the attachment or is it still pending approval
 
  • #3


laksate said:
can you guys access the attachment or is it still pending approval

Generally it's better to put in a link to the picture if you can.
 
  • #4


Well I only have the file, it is not available anywhere on the internet. The picture has been approved and now you guys can view the picture.

Can anyone help me with this problem?
 
  • #5
Welcome to PF!

Hi laksate ! Welcome to PF! :smile:
laksate said:
Now I have attached the solution from the solutions manual. However my problem with the solution is shouldn't it be considered that heat must be transferred to bring the temperature of the water up to 100 degrees C?

No … evaporation happens without any change in temperature …

even at "room temperature", some of the molecules are going fast enough to get away! :biggrin:

For some more detail, se http://en.wikipedia.org/wiki/Thermal_radiation :wink:
 

1. What is evaporative cooling?

Evaporative cooling is a process in which the temperature of a substance (such as a beverage) decreases due to the evaporation of its liquid molecules. This is caused by the transfer of heat energy from the liquid to the surrounding environment.

2. How does evaporative cooling work?

Evaporative cooling works by utilizing the principle of latent heat of vaporization. As the liquid molecules in a substance (such as a beverage) absorb energy from their surroundings, they gain enough energy to overcome the attractive forces between them and escape into the surrounding air as gas. This process of evaporation requires energy, which is taken from the remaining liquid, resulting in a decrease in temperature.

3. What factors affect the rate of evaporative cooling?

The rate of evaporative cooling is affected by several factors, including the surface area of the substance, the humidity and temperature of the surrounding environment, and the strength of the attractive forces between the liquid molecules. Additionally, the type of liquid, its initial temperature, and the air flow around the substance can also influence the rate of evaporative cooling.

4. How does evaporative cooling affect the taste of a beverage?

Evaporative cooling can affect the taste of a beverage by altering the balance of its ingredients. As the liquid evaporates, the remaining liquid becomes more concentrated, potentially changing the taste. Additionally, the decrease in temperature can also affect the perception of taste, as colder substances may taste less flavorful.

5. Can evaporative cooling be used to keep beverages cold?

Yes, evaporative cooling can be used to keep beverages cold. By taking advantage of the principle of latent heat of vaporization, the temperature of a beverage can be lowered through evaporation. This is commonly seen in evaporative coolers, where a fan blows air over a wet surface, causing the water to evaporate and cool the surrounding air. However, the effectiveness of this method may depend on the surrounding environment and other factors mentioned above.

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