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Unformatted text preview: Chapter 5 The First Law of Thermodynamics 5-191 Two identical buildings in Los Angeles and Denver have the same infiltration rate. The ratio of the heat losses by infiltration at the two cities under identical conditions is to be determined. Assumptions 1 Both buildings are identical and both are subjected to the same conditions except the atmospheric conditions. 2 Air is an ideal gas with constant specific heats at room temperature. 3 Steady flow conditions exist. Analysis We can view infiltration as a steady stream of air that is heated as it flows in an imaginary duct passing through the building. The energy balance for this imaginary steady-flow system can be expressed in the rate form as ( ) ( ) E E E E E Q mh mh Q mC T T VC T T in out in out in in p p- = = = + = 2245 2245 =- =- Rate of net energy transfer by heat, work, and mass system (steady) Rate of change in internal, kinetic, potential, etc. energies (since ke pe 0) 1 2 2 1 2 1 Then the sensible infiltration heat loss (heat gain for the infiltrating air) can be expressed ) ( ) )( ( ) ( building air , air on infiltrati o i p o o i p T T C V ACH T T C m Q- =- = where ACH is the infiltration volume rate in air changes per hour . Therefore, the infiltration heat loss is proportional to the density of air, and thus the ratio of infiltration heat losses at the two cities is simply the densities of outdoor air at those cities, 1.22 = = = = = = kPa 83 kPa 101 ) / ( ) / ( ratio loss heat on Infiltrati Denver , Angeles Los , Denver Angeles Los Denver air, , Angeles Los air, , Denver on, infiltrati Angeles Los on, infiltrati P P RT P RT P Q Q o o o Therefore, the infiltration heat loss in Los Angeles will be 22% higher than that in Denver under identical conditions. 5-177 Los Angeles: 101 kPa Denver: 83 kPa Chapter 5 The First Law of Thermodynamics 5-192 The ventilating fan of the bathroom of an electrically heated building in San Francisco runs continuously. The amount and cost of the heat vented out per month in winter are to be determined. Assumptions 1 We take the atmospheric pressure to be 1 atm = 101.3 kPa since San Francisco is at sea level. 2 The building is maintained at 22 C at all times. 3 The infiltrating air is heated to 22 C before it exfiltrates. 4 Air is an ideal gas with constant specific heats at room temperature. 5 Steady flow conditions exist. Properties The gas constant of air is R = 0.287 kPa.m 3 /kg K (Table A-1). The specific heat of air at room temperature is C p = 1.005 kJ/kg C (Table A- 2). Analysis The density of air at the indoor conditions of 1 atm and 22 C is 3 3 kg/m 20 . 1 K) 273 + /kg.K)(22 kPa.m 287 . ( kPa) 3 . 101 ( = = = o o o RT P Then the mass flow rate of air vented out becomes ( . )( . ) . m V air air 3 3 kg / m m / s kg / s = = = 120 0 030 0036 We can view infiltration as a steady stream of air that is heated as it flows in an imaginary duct passing through the...
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This homework help was uploaded on 04/18/2008 for the course EML 3007 taught by Professor Chung during the Spring '08 term at University of Florida.
- Spring '08