i’m just wondering how fluid & heat transfer works, if you mix water that is 20 or 30 degrees apart in temperature does the hot or cold have an advantage or does it meet in the middle and equalize?
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If you ignore the escaping heat or doing it in a very insulated container than the answer is yes it will be 65. Just multiply the degree with the mass, and divide it by total mass, which in this occasion is equal for both temperatures so just add the temperatures and divide by 2.
The formula for the heat capacity of an object (a bucket of water or a solid object) is mass times temperature.
So if you have 10 pounds of water at 50 degrees (irrelevant of Celcius, Fahrenheit or Kelvin) and 10 pounds of water at 80 degrees, the first one has a heat capacity of 10×50 = 500 and the second has a heat capacity of 10×80 = 800. Add them together (500+800 = 1300) and divide them by the new mass (10+10 = 20) and you end up with 65 degrees.
Now your question was in gallons of water, then you have to realize that objects which are hotter have a higher volume than objects which are colder[*] and as such the 10 gallons at 80 degrees will be lighter than 10 gallons at 50 degrees. At the volumes and temperature differences you work with, this is negligible, but if you are moving liquids around in a big tanker behind your truck in a hot day, then it’s important to remember this and take the volume/temperature difference into account.
But for you, working in theoretical and ideal situations, yes it will be 65 degrees Fahrenheit. Initially it will be colder/hotter on the outsides where the two liquids don’t touch, but overtime the energy of the liquid with the higher temperature will flow into the colder liquid and then everything will be the same.
Yup, they meet in the middle.
Funny enough, I studied almost this exact scenario in college, with respect to industrial processes. The scenario was, you want to fill a tank with water at a certain temperature, and you have a hot water line at one temperature and a cold water line at another temperature. You can precisely determine or control the temperature of the water in the tank by changing the ratio of hot water to cold water you’re pouring in.
It ends up very very close to *but not quite* in the middle.
Why you ask?
Two effects:
1. A liquid’s density decreases (*usually) with higher temperatures, so there’s slightly less mass of water in the hotter tank. If you asked the question in terms of mass, of course this wouldn’t be an effect.
2. Heat capacity, which is the amount of thermal energy required to change the temperature a unit amount changes with temperature too.
We’re only talking a tiny fraction of a percent off with liquid water, but if you were mixing steam these effects can be rather significant.
*Water is strange and is densest at 4C, most liquids are densest at freezing temperature. This means in the 0C to 4C range water gets denser as you heat it.
Yes, and if you mix 3 parts boiling water with 2 parts cold water or milk from the refrigerator you get `(3*212°F+2*36°F)/5 = 141°F` perfect temperature beverage.
It’s close enough, but not exactly. Your 40 gallons of water at different temperatures don’t even have the same mass. So while it’s close enough to correct for water at these temperatures, you shouldn’t assume it generalizes for all materials, where the specific heat or volume or any other factor can vary a lot more.
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