a)
The rate of exergy destroyed during the process and the exit temperature
a)
Answer to Problem 64P
The rate of exergy destroyed during the process is
The exit temperature
Explanation of Solution
Draw the schematic diagram of the flow of refrigerant-134a through evaporator section as shown in Figure (1).
Write the expression for the mass balances equation for the heat exchanger.
Here, mass flow rate of refrigerant at inlet is
Since net mass flow rate of refrigerant-134a and air through system is 0.
From Figure (1), the mass flow rate of refrigerant-134a at
Here, initial and final mass flow rate of refrigerant at
From Figure (1), the mass flow rate of air at
Here, mass flow rate of air at
Write the expression for the enthalpy at state 1
Write the expression for the entropy at state 1
Write the expression for the mass flow rate of air
Here, gas constant of air is
Write the expression for energy balance for the heat exchanger
Here, rate of net energy transfer in to the control volume is
Substitute 0 for
Here, mass flow rate at
Write the expression for the entropy balance for the steady flow system as;
Here, rate of entropy generation is
At steady state, rate of change in entropy of the system is zero.
Substitute 0 for
Here, entropy at
Write the expression for the change between state 4 entropy
Here, temperature at state
Write the expression for the exergy destroyed rate during the process
Here, dead state temperature is
Conclusion:
Refer to Table A-12, “Saturated refrigerant-134a-Pressure table”, obtain the following properties at the pressure
Here, enthalpy of saturated liquid is
Substitute
Substitute
Refer to Table A-12, “Saturated refrigerant-134a-Pressure table”, obtain the following properties at the pressure
Here, enthalpy at state 2 is
From the Table A-2, “Ideal-gas specific heats of various common gases table”, select the gas constant of air gas
Substitute
At steady state, rate of change in internal energy of the system is zero.
From the Table A-2, “Ideal-gas specific heats of various common gases table”, select the constant pressure specific heat
Substitute
Thus, the exit temperature
Substitute
Substitute
Substitute
Thus, the rate of exergy destroyed during the process is
b)
The exit temperature of the air and the rate of exergy destroyed during the process without insulation.
b)
Answer to Problem 64P
The exit temperature of the air without insulation is
The rate of exergy destroyed during the process without insulation is
Explanation of Solution
Write the expression for the state 4 temperature
Here, heat gain is from the surrounding
Write the expression for the entropy balance For an extended system as;
Conclusion:
Substitute
Thus, the exit temperature of the air is
substitute
Substitute
Substitute
Thus, the rate of exergy destroyed during the process is
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Chapter 8 Solutions
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