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Determine the energy needed to quench a hot gas with water

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Assume we have a 100,000 cubic foot per minute gas (air) stream at 700 degrees F that goes to an air pollution control device; also assume the hot air has no moisture content.

If 50 degree F cooling water is used, and the desire is to cool the hot air from 700 degrees F to 175 degrees F, how much 50 degree F water is needed to quench the gas? And what would be the final temperature of the cooling/quench water after it has cooled the gas?

Assume atmospheric pressure prevails.

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The energy needed to quench a hot gas with water is calculated.

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For 100% efficient heat exchanger we have:
Qair = Qwater

but Qair = mcdeltaT
m = 100,000 ft^3/min = 100,000 ft^3/min*density of air
Here the air changes from 700F to 175F. So we need to use the density of air at the mean temperature 875/2 = 437F. At this temperature, density of air = 0.089(lb/ft^3) (see reference 1)
Thus m = 100,000*0.089 = 8900 (lb/min)
c = specific heat of air at ...

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