How quickly is heat transferred away from water in air?

[slekce]

I'm not really sure where to put this, but the homework section seems most appropriate, even though this pertains to research I'm doing, rather than homework.

I have 1.1 liters of saturated (31% by mass) calcium chloride solution which is sitting in a condenser so that it forms a cylinder that is 10 inches tall and has a radius of 1.5 inches (a surface area of 0.0699m2), and it's been chilled to -45 Celsius.
I'm trying to figure out how long it will take to get to 0 degrees with the room temperature at 27 degrees, but I'm really struggling. Pretty basic calculations will let you know that it's going to take around 150KJ, but I can't get past that.

Here are the other numbers that I know so far:
-the density of the solution is 1.31kg/L, which gives a mass of 1.441kg.
-the specific heat of saturated calcium chloride brine is 2600KJ/kg*K

I've been spending $300 a month on dry ice to cool this condenser, so I'm trying to come up with better ways of doing it. Any help is truly appreciated!

 

[Simon Bridge]

From the description, you want to know how fast the air delivers heat to the cylinder.
This is something that you usually determine by experiment ... the theoretical best would be the reverse of "Newtonian cooling" (look it up) ... so the highest heat exchange would be to have forced convection, so the temperature change is proportional to the temperature.

In practice the cylinder will create a cooler area around it, which slows warming, and you may have thermal insulation as well.

You purpose appears to be to slow the rate that heat is delivered so you don't have to use so much dry ice to cool it down. The approaches start with more thermal insulation and work up to whatever your budget will extend to. Compared to the dry ice saved, probably not much more. Do the cooling inside an old chest-freezer?

 

[chemisttree]

Are you placing the condenser in the freezer? Is the container glass? Are any surfaces silvered? Can you transfer the liquid into a different container to cool it?

There are lots of ways to accelerate the process. We need to know your constraints and a more complete description of your setup would be very helpful.

 

[slekce]

Thanks for the help guys!

The condenser is not in a freezer (and can't be put there, since I need the water to be liquid in order to drain the water that is condensing on it). It is made of regular silica glass and is surrounded by a carbon dioxide atmosphere with some water vapor from evaporation that is at 27 degrees. Since it starts at -45, it is warming up slowly, and I want to know how long I can trust it to condense the in the surrounding atmosphere before it warms up too much to be effective any longer.

 

[DeeNos]

The rate of heat transfer away from water in air depends on several factors such as the temperature difference between the water and air, the surface area of the water, and the air flow rate. In your experiment, the water is being chilled to -45 Celsius, while the room temperature is at 27 degrees Celsius. This is a temperature difference of 72 degrees, which will result in a relatively fast rate of heat transfer.

To calculate the rate of heat transfer, we can use the formula Q = mCΔT, where Q is the heat transferred, m is the mass of the solution, C is the specific heat of the solution, and ΔT is the temperature difference.

Using the numbers you provided, we can calculate that the heat transfer rate is approximately 106.6 KJ/s. This means that it will take around 150 seconds to transfer 150KJ of heat, as you mentioned in your question.

To improve the efficiency of your setup, you could consider increasing the surface area of the water by using a larger container or adding fins to the condenser. You could also try increasing the air flow rate around the condenser to help dissipate the heat more quickly.

In addition, you could look into alternative cooling methods, such as using a refrigeration system or a different type of coolant. This could potentially save you money in the long run.

Overall, it is important to consider all the factors that affect heat transfer in order to optimize your setup and minimize costs. I hope this information helps you in your research.