Atmospheric air at 1 atm, 32°C, and 95 percent relative humidity is cooled to 24°C and 60 percent relative humidity. A simple ideal vapor-compression refrigeration system using refrigerant-134a as the working fluid is used to provide the cooling required. It operates its evaporator at 4°C and its condenser at a saturation temperature of 39.4°C. The condenser rejects its heat to the atmospheric air. Calculate the exergy destruction, in kJ, in the total system per 1000 m3 of dry air processed.
The exergy destruction in the total system per
Answer to Problem 86P
The exergy destruction in the total system per
Explanation of Solution
Show the T-s diagram for the simple ideal vapour-compression refrigeration system.
Express the mass of air.
Here, volume at state 1 is
Express the water mass balance and energy balance equations to the combined cooling and dehumidification section.
For water mass balance:
For energy balance:
Write the energy balance equation using steady-flow equation.
Here, the rate of total energy entering the system is
Substitute
Here, the specific enthalpy at the state 1 and 2 are
Write the formula for mass flow rate of refrigerant-134a.
Write the formula for amount of heat rejected from the condenser.
Calculate the exergy destruction in the components of the refrigeration cycle.
For the process 1-2,
Here, the process 1-2 is an isentropic.
For the process 2-3,
For the process 3-4,
Write the entropy change of water vapour in the air stream.
Write the entropy of water leaving the cooling section.
Determine the partial pressure of water vapour at state 1 for air steam.
Determine the partial pressure of dry air at state 1 for air steam.
Here, the pressure at the state 1 is
Determine the partial pressure of water vapour at state 2 for air steam.
Determine the partial pressure of dry air at state 2 for air steam.
Here, the pressure at the state 2 is
Write the formula for entropy change of dry air.
Write the formula for entropy change R-134a in the evaporator.
Write the formula for an entropy balance on the evaporator.
Write the formula for an exergy destruction in the evaporator.
Write the formula for the total exergy destruction.
Conclusion:
Refer Figure A-31, “psychometric chart at
Refer Table A-4, “saturated water-temperature table”, and write the specific enthalpy of condensate water at temperature of
Here, entropy of saturation liquid at temperature of
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y is temperature and specific enthalpy of condensate water at state 2 respectively.
Show the specific enthalpy of condensate water at corresponding to temperature as in Table (1).
Temperature |
Specific enthalpy of condensate water |
25 | 104.83 |
28 | |
30 | 125.74 |
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Substitute 1105 kg for
Substitute 1105 kg for
From the Table A-11 “Saturated Refrigerant-134a-Pressure Table”, obtain the value of the specific enthalpy and entropy at state 1 of
Refer Table A-13 “Saturated Refrigerant-134a-Pressure Table”, and write the specific enthalpy at state 2 in 1 MPa of pressure and entropy of
From the Table A-12 “Saturated Refrigerant-134a-Pressure Table”, obtain the value of the specific enthalpy and entropy at state 3 of
Here, the specific enthalpy at the state 4 and 3 are equal in the throttling.
Calculate the value of
From the Table A-11 “Saturated Refrigerant-134a-Pressure Table”, obtain the value of the specific enthalpy and entropy of saturated liquid and change upon vaporization at state 4 of
Substitute
Calculate the value of specific entropy of the state 4.
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Refer Table A-4 “Saturated water-temperature Table”, and write the specific entropy at state 1 at
Refer Table A-4 “Saturated water-temperature Table”, and write the specific entropy at state 1 at
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Substitute 0 for
Thus, the exergy destruction in the total system per
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Chapter 14 Solutions
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