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# Physics riddle

Ranch Hand
Posts: 974
11
Say I want to have one liter of water of 70 degrees Celsius, how much water of room temperature (20 C) and boiling water (100 C) must I mix?

I am puzzling with that myself at the moment. I want to disinfect something made of plastic. 100C would be too much for it.

Sheriff
Posts: 4709
309
Interesting puzzle, and one to which I don't know the answer. But, I've heard that the resulting temperature depends on whether you pour hot liquid into cold, or cold liquid into hot. (Note: I have no knowledge or evidence to back this up so I'll be accepting no follow up questions). I think this forms the foundation of some peoples arguments on the correct way to make a cup of tea: Milk first (hot tea on cold milk) or milk last (cold milk on hot tea).

Marshal
Posts: 7346
498
Also need to take into consideration the container material and its size where water going to be poured as it will absorb some of the heat.

Tim Cooke
Sheriff
Posts: 4709
309
Oh this is getting really hard really quickly. Might I recommend pouring the boiled water from the kettle into a glass jug and letting it cool to the desired temperature. A thermometer might be required, unless you're happy to guess at some "hot but not boiling" temperature.

Jan de Boer
Ranch Hand
Posts: 974
11
Well maybe this helps:

https://en.wikipedia.org/wiki/Calorie

So since the amount of energy to warm 1 liter of water one degree Celsius is more or less constant between zero and boiling point, you would have to solve:

20 * X + 100 * Y = 70

At least that is what I think.

Bartender
Posts: 1868
81
Some what related to this is measuring gasoline. You pay by liter or gallon usually, and liquid changes size at different temperatures.
I believe that prices in Canada are corrected at four degrees Celsius for most automotive gasoline/fuel.

Jan de Boer
Ranch Hand
Posts: 974
11

Tim Cooke wrote:Oh this is getting really hard really quickly. Might I recommend pouring the boiled water from the kettle into a glass jug and letting it cool to the desired temperature. A thermometer might be required, unless you're happy to guess at some "hot but not boiling" temperature.

I do not have a thermometer.

I was counting on you guys!

Marshal
Posts: 66951
255
You don't need a thrmometer, but a barometer might be useful to confirm your boiling wter is at 100°C.
Jan de Boer was right, well almost:-
100x + 20y = 70 × (x + y)
Make x + y equal to 1000 and solve the equation. It is what was called simultaneous equations when I was twelve.

I can think of another way to solve the mystery,

Campbell Ritchie
Marshal
Posts: 66951
255

Pete Letkeman wrote:. . .  prices in Canada are corrected at four degrees Celsius for most automotive gasoline/fuel.

We must have a warmer climate; ours are corrected to 15°C.

The simple formulae will give approximate results, and the end result will vary slightly depending on whether you measure the water in a jug or weigh it.

Jan de Boer
Ranch Hand
Posts: 974
11

Campbell Ritchie wrote:Make x + y equal to 1000.

Yeah well. 1000 ml, 1 liter... ;)

But this should basically work right? Because then I will use it.

Jan de Boer
Ranch Hand
Posts: 974
11
100x + 20y = 70
x+y = 1
So I replace y with 1-x
100x + 20 - 20 x = 70
80x = 50
x=5/8 liter.

Check:

100*(5/8) + 20* (3/8) = 70
62.5 + 7.5 = 70

And I am mixing the waters! Thanks! :-)

Jan de Boer
Ranch Hand
Posts: 974
11

Campbell Ritchie wrote:I can think of another way to solve the mystery,

Which would be?

Campbell Ritchie
Marshal
Posts: 66951
255
You want to heat the water from 20° to 70°.
You want to cool the water from 100° to 70°.
That reduces to 5 units of heating and 3 units of cooling.
So you want 5 parts of hot water and 3 parts of cold water. 5 + 3 = 8 So you want ⅝ of one (=625ml) and ⅜ of the other (=375ml).

Jan de Boer
Ranch Hand
Posts: 974
11

Campbell Ritchie wrote:That reduces to 5 units of heating and 3 units of cooling.

The 5 deduced from 70-20, and the 3 from 100-70? Okay.

So for example if I want to do my laundry at 60 max, I would mix equal parts of boiling hot and room temperature water. I see camping possibilities here.

Campbell Ritchie
Marshal
Posts: 66951
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Do you wash clothes when camping? Can you get cold water as warm as 20°? Yes, you probably can, but more like 20°F than 20°C
I use a similar technique for baking bread: mix equal volumes of cold and boiling water and whisk the sugar and yeast into the water. I think you will find that is a common technique in bread recipes.

Jan de Boer
Ranch Hand
Posts: 974
11

Campbell Ritchie wrote:Do you wash clothes when camping? Can you get cold water as warm as 20°? Yes, you probably can, but more like 20°F than 20°C .

20°F would be frozen. That would be another calculation. You would have to calculate the energy to get the ice to zero degrees, and then calculate the melt warmth and add it. As last you would have to do the same calculation as above. That is a new challenge.

Looks like nerd camp meets girls scouts here! ;)

Campbell Ritchie
Marshal
Posts: 66951
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I said nearer; 32.1°F is nearer to 20° than it is to 20°C (68°F).
You think you can get girls to warm up the water for you? No chance.

Jan de Boer
Ranch Hand
Posts: 974
11

Campbell Ritchie wrote:You think you can get girls to warm up the water for you?

No I will warm up the water, and they will do the laundry! But seriously, girls, girl scouts too probably, like smart boys. Especially when they are a little rebellious, creative and witty. At least that is my high school experience. I will blind them with science!

lowercase baba
Posts: 12781
51
• 1
here's how I'd do it...

x = grams cold water
y = grams hot water

x+y = 1000

so far, so good.  So the heat added to the cold water has to equal the heat lost by the warm water.  The warm water cools 30 calories per gram. The cold water must be heated 50 calories per gram. so...

50x == 30y

so ultimately, x = 375 grams, y = 625 grams.

Tim Cooke
Sheriff
Posts: 4709
309
Jan, have you done any experiments yet to validate or debunk these theories?

Campbell Ritchie
Marshal
Posts: 66951
255
Which theory? The one about keeping girls warm?

Jan de Boer
Ranch Hand
Posts: 974
11
Tim, I have used the calculation, yes. But I have no proof, I wanted to know if I could do this because I have no thermometer. So I have not checked if the temperature is right, just assumed that it would be.

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