Question 53522: Water temp. coming into the house is 60 degrees f, some of the water goes into the hot water heater, which reaches 120 degrees f, you fill a bath tub with 22 gallons of water with a temp. of 80 degrees f. What is the volume of cold water and the volume of hot water.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Water temp. coming into the house is 60 degrees f, some of the water goes into the hot water heater, which reaches 120 degrees f, you fill a bath tub with 22 gallons of water with a temp. of 80 degrees f. What is the volume of cold water and the volume of hot water
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There is alot of assuming here regarding thermodynamics but here goes.
Let the amount of heated water be "x" ; its heat content is 120x
The amount of unheated water is "22-x" ; its heat content is 60(22-x)=1320-60x
The amount of mixed water is 22 gallons ; its heat content is 80(22)=1760
EQUATION:
heat + heat = heat
120x + 1320-60x = 1760
60x == 440
x=7 1/3 gallons of hot water
22-x= 14 2/3 gallons of unheated water
Cheers,
Stan H.
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