Mixing three water quantities at different temperatures

In summary, the person is trying to figure out how to mix three quantities of water to achieve a desired final temperature and volume. They have equations for mixing two quantities but not three, and are seeking help to solve the problem. They provide details of their initial quantities and desired results, and another person suggests solving two simultaneous equations to find the answer. The original person then clarifies their question and thanks the other person for their help.
  • #1
beer_brewer
3
0
I am trying to figure out the following in my beer brewing. I have been able to find equations for mixing two quantities of water, but not three. Can anyone help me out here?

So, I have 5 liters at 100 C and I want to add 18 liters (x at 20 C and y at 8 C) to arrive at 23 liters at 24 C. This is because most of the remaining 18 liters is at room temperature (20 C), and I want to find out how much water chilled in the fridge (8 C) will bring me to the desired 23 liters at 24 C?

many thanks
 
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  • #2
Solve the two simultaneous equations the answer is in litres. This assumes that all the liquid is water but I guess that the hot liquid is wort which probably has a higher specific heat capacity then pure water in which case the final mixture will be hotter then intended, these should get you fairly close though.

X+Y=19

293X+281Y=4966
 
  • #3
Thanks Jobrag, but I need some clarification. Why is X + Y = 19 and not 18? And how did you get the second equation. When I put X = 19 - Y into the second equation (which I assume you meant this when you said to calculate both equations simultaneously) I ended up with X=50.08.

cheers
 
  • #4
beer_brewer said:
I have been able to find equations for mixing two quantities of water...

OK - you want to mix 5 liters at 100C with 18 liters, to get 23 liters at 24C. What must be the mixed temperature of those 18 liters?

Once you get that figured out, you should be able to figure out how to make up the 18 liters. But I will give you a hint, or rather a prediction: you aren't going to be able to do what you want (your cold water isn't cold enough).
 
  • #5
Ah ha. That explains the 50 liters. Thank you. I was letting my assumptions get in the way of the calculation.
 

1. What is the best way to mix three water quantities at different temperatures?

The best way to mix three water quantities at different temperatures is to start by pouring the coldest water into a container, followed by the warmer water, and then the hottest water. This will help to gradually bring all three temperatures closer together and prevent drastic temperature changes.

2. Can I mix hot and cold water together to get a warm water mixture?

Yes, you can mix hot and cold water together to get a warm water mixture. However, it is important to note that the resulting temperature will depend on the proportions of hot and cold water used. To achieve a specific temperature, it is best to use a thermometer to measure and adjust accordingly.

3. How long does it take for three water quantities at different temperatures to reach an equilibrium?

The time it takes for three water quantities at different temperatures to reach an equilibrium can vary depending on the volume and temperature differences of each quantity. In general, it can take anywhere from a few minutes to half an hour for the water to reach a consistent temperature.

4. Can I mix three water quantities at different temperatures in any type of container?

Yes, you can mix three water quantities at different temperatures in any type of container. However, it is important to consider the material of the container, as some materials may affect the rate at which the water temperatures equilibrate. Glass and metal containers are typically better at conducting heat, while plastic containers may insulate the water and slow down the mixing process.

5. How does the order in which I mix the three water quantities affect the final temperature?

The order in which you mix the three water quantities can have an impact on the final temperature. Generally, adding the coldest water first and then the warmer water will result in a lower final temperature, while adding the warmer water first and then the colder water will result in a higher final temperature. This is because the temperature differences are more significant when the colder water is added first.

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