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# Heat energy needed to raise water temperature from 50 degrees F to 212 degrees F?

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100 gallons per minute flow of water at 50 degrees F passes through a theoretically 100% efficient heat exchanger. The hot side or energy to the heat exchanger is a 510 degree F hot gas (essentially steam).

Assuming the 510 degree hot gas will heat the water, what is the energy in BTU's needed to accomplish and what would the hot gas flow rate at 510 degrees need to be to perform this heating?

https://brainmass.com/engineering/process-engineering/heat-energy-needed-raise-water-temperature-129759

#### Solution Preview

The heat exchange in the 100% efficient unit is:
Qwater = Qgas
(mcdeltaT)water = (mcdeltaT)gas

Thus we can calculate the heat needed to transfer to the water:
Qwater = mcdeltaT
m = 100 gpm = 833 (lb/min)
c = 1 Btu/lb.F
deltaT = 212 - 50 = 162 ...

#### Solution Summary

The heat energy required to turn liquid water in to steam is calculated. The energy in BTU's needed to accomplish and what would the hot gas flow rate at 510 degrees need to be to perform this heating is examined.

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## Applying to Ideal Gas Equation

In our course lab, our experiment required us to take wood fibers and mix them into a slurry in which that slurry was 65% water content. We then formed the slurry into a brick and placed it in a small electric lab press where variable hydraulic pressure and heat energy was applied to this wet wood brick.

Using a thermocouple and pressure probe, we measured the internal temperature and gas pressure in the core of this wooden brick.

I have attached the data file and the graph which shows the application of hydraulic energy and the resultant core temp and internal gas temp as a function of time in this little lab press.

Assuming the water vapor is behaving like an ideal gas, we are asked to explain how PV=nRT can be used to derive the unknown gas volume with the information at hand. In this case, we neither know V or n - how can this be solved given the information at hand. The wet weight of the sample brick at 65% moisture content is assumed as 15 lbs.

Can you show me how the formula would apply at a few of the data points so that I can see how the volume of the gas is derived?

Also, would it be true that as core gas pressure increased that it would take more and more heat energy to boil off the water in the core? Why?

Thank you

The other info that I left out was that the heat provided from the lab press was a constant 400 degrees F. The wood slurry sample was 12" x 12" x 2" thick - upon being pressed, and as the data indicates, water began to boil off at and above 212 F and a clear increase in gas vapor pressure and increase in core gas temperature occurred. This cycle in the press, the combination of the hydraulic pressure and temperature is supposed to represent a medium density fiberboard process where hydraulic pressure is supposed to dewater some of the sample in the early stage of the cycle, but heat energy does most of the dewatering. I was surprised however to see gas vapor pressures this high from the boil off and partial entrapment of the water vapor. That is all of the info I have.

Hope you can help.

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