1. The problem statement, all variables and given/known data 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. Given values: 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 2. Relevant equations PV = mRT E in - Eout = change in energy of the system 3. 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. So: 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?