A house with floor space of 2000 ft^2 and average height of 9 ft is heated from an average temperature of 50 degrees F to 70 degrees F. Determine the amount of energy transfered in the house assuming:
a) The house is air tight.
b) Some air escapes through the cracks as the heated air in the house expands at constant pressure.
Floor space = 2000 ft^2
Height = 9 ft
Atmospheric pressure = 12.2 psia
Thermodynamic properties of air:
Gas constant R = 0.3704 psia ft^3/(lbm R)
Cv = .171 BTU/lbmR
Cp = 0.240 BTU/lbmR
PV = mRT
E in - Eout = change in energy of the system
The Attempt at a Solution
Part a is relatively simple. Since we are treating the house as an airtight, constant volume, the equation for this would be:
Qin = mCv*(T2-T1)
where mass m = PV/RT = 1162.4 lbm, then
Ein = Qin, Eout = 0:
Qin - 0 = change of energy in the system
Qin = 1162*(.171)*(20) = 3974 BTU
Part B is where I'm a bit unsure of. I feel there is some missing information.
Since air leaks, we should have a loss of mass in the system, right? So we should have on the energy equation:
m1*qin - m2*qout = m3*cp*(T2-T1)
where q denotes heat per unit mass.
Which would mean energy is lost through mass transfer. Is this correct?
Using the ideal gas law, m1T1 = m3T3, so the mass remaining in the house after expansion would be:
m3 = 1118.6 lbm
Meaning m2 = 1162-1119 = 43 lbm.
1162lbm*qin - (43lbm)*qout = (1118.6lbm)*(0.240 BTU/lbmR)*20R
1162qin - 43qout = 5369 BTU
But this leaves me with two unknowns and one equation. Should it be assumed that the amount of energy lost through the cracks is negligible?