Quote:
Originally posted by kutulu
for 500 gallons from 75 to 95, my answer was 85 gallons:
Energy balance:
m1*Cp*(Tf - Ti) = m2*Cp(Tb-Tf)
m1 = mass of water in tub
Cp = heat capacity (assumed constant)
Tf = 95F
Ti = 75f
m2 = mass of water needed
Tb = 212
The equation reduces to:
m2 = m1*(Tf - Ti)/(Tb - Tf)
a cool thing about this eq is that it as long as the volume is not a funtion of temperature (you can assume it is not) you can use any units you want to use for the temp. You can also interchange volume and mass (using any units) and get the same answer.
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You also have to assume the system is adiabatic, which it is obviously not since the hot tub is open to the air, but if you pour in the water quickly, it shouldn't make that big of a difference.