# Energy Transfer question



## seafolly (Jun 17, 2010)

Some wise soul here suggested I post this question in case anyone might have the brain power to help a gal out.  This isn't a homework help forum but still, a lot of you are pretty math oriented and might get this.

_A heat exchanger is used to warm apple cider using steam as the heat source. The cider is heated from an initial temperature of 4°C to a final temperature of 65°C. The steam enters the heat exchanger as 50% quality steam and exits as water condensate at 85°C. Calculate the mass of steam required to heat 150 kg of cider. (For the cider, assume the Cp=3.651 kJ/kg°C, and latent heat=280.18 kJ/kg.) _

So. I understand the latent heat info is kind of redundant. I'm hoping someone might be able to tell me if I'm on the right track?

1. Qcider=mCpT
Q = (150 kg)(3.651 kJ/kg)(61 C)
= 33,406.65

2. Calculate enthalpy to convert 50% of the water to steam
(0.50) x (2257.06 kJ)
= 1,128.53 kJ

3. Mass of steam...whut? Maybe it's because it's past 2 am and I've been researching all day but HELP. I know the answer is supposed to be near 30 but I haven't gotten there yet...clearly.


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## lonelyjew (Jan 20, 2010)

What temperature is the steam? I should be getting to bed so I'm sorry if I missed something, but if you have the steam's starting temperature, and you know the end temp of the steam, and the total energy necessary to heat the cider, you should be able to calculate it with mass of cider x specific heat x (65C - 4C) = mass of steam/water x (specific heat of steam x (starting temp - 100C) + heat given off in condensation + specific heat of water x (100C - 85C))

edit* 
Does 50% quality steam mean only 50% of it enters as steam? If so then scrap the steam temp as you know it should be 100C. Half of the mass will have to condense, to it would be mass/2 x heat given off when steam condensates to water, and then mass x (100C - 85C) as all of the water is cooled to 85C from 100C. Total energy of that sum should equal the energy needed to heat the cider to 65C.

edit 2*

Already going to wake up hating myself, so might as well type the equation -

Qcider = Mass H2O x (.5 x enthalpy change in condensation + specific heat of water)


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## cavemanslaststand (Jan 6, 2011)

lonelyjew said:


> ...
> 
> edit*
> *Does 50% quality steam mean only 50% of it enters as steam?* If so then scrap the steam temp as you know it should be 100C. Half of the mass will have to condense, to it would be mass/2 x heat given off when steam condensates to water, and then mass x (100C - 85C) as all of the water is cooled to 85C from 100C. Total energy of that sum should equal the energy needed to heat the cider to 65C.
> ...


*edit** description was perfect! Yes, that's exactly what it means. 50% quality steam means half vapor in equilibrium with liquid water. Equilibrium temp is 100oC for normal atmosphere.

Then *edit 2** was very close to *edit** except some details were missing:

Qcider = QtotalH20
33,406.65 kJ = 0.5 * m * (2250.57 kJ/kg) + m (CpH20) (100 - 85)


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## seafolly (Jun 17, 2010)

Holy cow. I didn't expect anyone to actually want to give it a shot. You two are fantastic. Thank you very much for explaining this! Now I need to get a cup of coffee before I sit down and stare at it to make it make sense.  Was my step 2 irrelevant?


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## Ape in space (May 31, 2010)

sorry, messed up the attachment when I uploaded... here it is again.
Also the convention I'm using means that delta T for water is -15.
EDIT: And that m_s in the 3rd last line and in the 2nd line is a typo... it's supposed to say m_(H2O).


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## seafolly (Jun 17, 2010)

WHAT. Seriously? You're in Toronto, right? I owe you cookies. Pick a flavour!


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