How much energy required = formula required please

[uk_vette]

Hi all,

I am stuck on a formula.

A fan extracting 100,000 litres of air in 24 hours.

Extracted air temperature is 20 deg,
Replacement cold inlet air is 8 deg.

How much energy is required in to heat this 100,000 litres of air back from 8 deg to 20 deg.

vette

[stevesingo]

Based on Dry air @ 20 degC.

Density of Air= 1.205kg/m3

Specific heat capacity of dry air= 1.006kJ/kg/K

Temp Delta 20-8=12

100,000lt = 100m3

100 * 1.205= 120.5kg

120.5*1.006*12= 1454.7 kJ

1kJ=0.277wHr

1454.7*0.277=403wHr

I think


Add in humidity and it will be more.

[AW111]

I think that the water vapour will require a fair bit more energy, but am too tired to work it out tonight.

[Mave]

Specific heat capacity of water vapour is about twice that of dry air - so if you know the relative humidity you can just factor up proportionally unless you're starting saturated :-)

[stevesingo]

stevesingo said:

Based on Dry air @ 20 degC.

Density of Air= 1.205kg/m3

Specific heat capacity of dry air= 1.006kJ/kg/K

Temp Delta 20-8=12

100,000lt = 100m3

100 * 1.205= 120.5kg

120.5 * 1.006*12= 1454.7 kJ

1kJ=0.277wHr

1454.7*0.277=403wHr

I think


Add in humidity and it will be more.

Referencing this

http://www.tis-gdv.de/tis_e/misc/klima.htm

At 10 degC 100% reletive humidity you will have 9.4g water per 1m3 of air.

So in addition to the dry air we need to calculate how much energy to heat the water suspended in the incoming air.

SHC of water =4.1813kJ/kg/k

100m3 of air

9.4g * 100= 940g or 0.94kg of water

0.94*4.18*12+= 47.15kJ

47.15 * 0.277= 13.1wHr

403+13.1= 416.1 wHr

Awaits corrections!

[uk_vette]

Thanks everyone.

So If say it is "roundabout" 420 wH I guess that's close enough for my calculations for now.

So with single phase domestic electricity here costing 14,9 pence per unit, that pans out to
14,9p for 1000 watts for 1 hour

Am I close to say that to "re-heat" the incoming air from 8 deg to 20 deg, would cost
about 7 pence per 24 hours?

vette

[stevesingo]

If your heater is 100% efficient, yes.

[caziques]

Pass the incoming and outgoing air through a quality heat exchanger and recover up to 90% of the energy for free. Do the last bit of heating with a heat pump for even more efficiency.

The complicated part is working out the cost effectiveness of such a system - energy saved versus capital cost.