Terry wrote:

Moving a pound of 55 F 100% RH basement air with 0.0093 pounds of
water vapor up into an airtight house and warming it to 65 with
0.24(65-55) = 2.4 Btu and drying it to 30% RH so it contains 0.004
pounds of water, releasing 1000x5.3 = 5.3 Btu, provides 5.3-2.4 = 2.9
Btu more heat than the electrical energy needed to operate the
dehumidifier.

One pound of air containing 0.0093 pounds of water
raised by (65-55)= 10 deg. F = 0.093 BTU?

No... Air has a specific heat of 0.24 Btu/lb-F, so raising a pound of air
(ignoring the small amount of water) 10 F takes 2.4 Btu.

Drying (removing) out the water from 100 to 30 per cent = 0.0093 * 0.7 =
0.0065 lbs.

No... 65 F air at 30% RH has Pa = 0.6e^(17.863-9621/(460+50)) = 0.189 "Hg, so
wi = 0.62198/(29.921/Pa-1) = 0.004, ie a pound of that air contains 0.004
pounds of water vapor.

Heat released from that 0.0065 lbs of water would be .....................

No... It takes 1000 Btu to evaporate a pound of water, so condensing
0.0093-0.004 = 0.0053 pounds of water out of that air releases 1000x0.0053
= 5.3 Btu, but heating the air from 50 to 65 requires 2.4, so the net heat
gain is 2.9, unless we use a simple air-air heat exchanger to warm upcoming
basement air up to about 65 with replacement room temp air that cools to
about 50 on the way down to the basement.

Nick