Hello!
I have a problem, but since this isn't for school I figured I wouldn't put it in the homework section. Okay, so here it is:
I need to calculate the resultant temperature of two bodies of water mixed together. The issue is that this is not a classic mixing two liquids in a beaker scenario. The complication is that the two bodies of water are the bottom of a reservoir and an input pipe. Because this is an open system, any water added by the input pipe will mix with the bottom of the lake (and yes, only the bottom because we need to maintain the natural stratification of the lake) without changing the volume of the lake because any water added to the system will be displaced and sent out of the reservoir over the dam. So I think I am dealing with mixing two bodies of water with different temperatures but a fixed final volume(The volume of the bottom layer of the lake). I know the classic heat formula Q=c*m*(T2-T1) and the resulting temperature formula for mixing two liquids Tf=(Va*Ta)+(Vb*TB)/(Va+Vb) but am confused by what to do about the volumes.
I suppose theoretically the masses will fully exchange and equalize their heats at the bottom of the reservoir before any water is displaced over the dam, so I could use the classic Tf formula, but I am unsure.
Right now I have done the calculations by calculating the heat in the bottom of the reservoir using an assumed reference start temp of 0 degrees and the final temp as the known average temperature of the bottom layer of the reservoir. Then I calculate the heat present in the pipe outflow for a certain volume of outflow by again using 0 degrees as a reference temperature. I then use the Tf=(Va*Ta)+(Vb*TB)/(Va+Vb) formula to calculate the resultant temperature of the mixed water.
Is this correct? What do you think???
Anne
