Explanation As the process is a steady flow and thus the mass flow rate of dry air remains constant during the entire process. m ˙ a 1 = m ˙ a 2 = m ˙ a Here, the mass flow rate of air at inlet is m ˙ a 1 , mass flow rate of dry air at exit is m ˙ a 2 and mass flow rate of dry air is m ˙ a . Express the mass flow rate of dry air. m ˙ a = ν ˙ 1 v 1 = ν car ACH v 1 (I) Here, volume flow rate at inlet is ν ˙ 1 , specific volume at inlet is v 1 , volume of the passenger compartment is v car and air changes per hour is ACH . Express the mass flow rate of vapor at inlet. m ˙ v 1 = ω 1 m ˙ a (II) Here, specific humidity at state 1 is ω 1 . Express the mass flow rate of vapor at exit. m ˙ v 2 = ω 2 m ˙ a (III) Here, specific humidity at state 2 is ω 2 . Express the rate of condensation of water. m ˙ w = m ˙ v 1 − m ˙ v 2 (IV) Express the enthalpy of condensate water. h w 2 = h f @ 10 °C (V) Here, enthalpy of saturation liquid at temperature of 10°C is h f @ 10 °C . Express the rate required heat transfer rate from the atmospheric air to the evaporator fluid from an energy balance on the control volume. m ˙ a h 1 = Q ˙ out + m ˙ a h 2 + m ˙ w h w 2 (VI) Here, enthalpy at state 1 and 2 is h 1 and h 2 respectively, and the rate required heat transfer rate is Q ˙ out . Conclusion: Show the psychrometric diagram as in Figure (1). Hence, the psychrometric diagram is shown in Figure (1). In Figure (1), the process line between states 1 and 2 cannot be shown as the process path is unknown. Refer Figure A-31, “psychometric chart at 1 atm total pressure”, and write the properties corresponding to dry bulb temperature of 27°C and relative humidity of 50% . h 1 = 55.60 kJ / kg dry air ω 1 = 0.01115 kg H 2 O / kg dry air ν 1 = 0.8655 m 3 / kg dry air T dp1 = 15.7 °C T wb1 = 19.5 °C Here, the dew-point and wet-bulb temperatures at the inlet are T dp1 and T wb1 respectively. Hence, the dew-point and wet-bulb temperatures at the inlet are 15 .7°C and 19 .5°C respectively. Refer Figure A-31, “psychometric chart at 1 atm total pressure”, and write the properties corresponding to dry bulb temperature of 10°C and relative humidity of 90% . h 2 = 27.35 kJ / kg dry air ω 2 = 0.00686 kg H 2 O / kg dry air Substitute 2 m 3 / change for ν car , 5 changes / min for ACH and 0.8655 m 3 / kg dry air for ν 1 in Equation (I). m ˙ a = ( 2 m 3 / change ) ( 5 changes / min ) 0

8th Edition

ISBN: 9780073398174

Author: Yunus A. Cengel Dr., Michael A. Boles

Publisher: McGraw-Hill Education

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Chapter 14.7, Problem 85P

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Sketch the psychrometric diagram; determine the dew-point and wet-bulb temperatures at the inlet, the required heat transfer rate and the rate of condensation of water vapor.

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Chapter 14.7, Problem 84P

Chapter 14.7, Problem 86P

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Chapter 14 Solutions

Thermodynamics: An Engineering Approach

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Sketch the psychrometric diagram; determine the dew-point and wet-bulb temperatures at the inlet, the required heat transfer rate and the rate of condensation of water vapor.

Solution Summary: The author illustrates the psychrometric diagram by determining the dew-point and wet-bulb temperatures, the required heat transfer rate, and the rate of condensation of water vapor.

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Sketch the psychrometric diagram; determine the dew-point and wet-bulb temperatures at the inlet, the required heat transfer rate and the rate of condensation of water vapor.

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Chapter 14 Solutions