An air-conditioning system involves the mixing of cold air and warm outdoor air before the mixture is routed to the conditioned room in steady operation. Cold air enters the mixing chamber at 7°C and 105 kPa at a rate of 0.55 m3/s while warm air enters at 34°C and 105 kPa. The air leaves the room at 24°C. The ratio of the mass flow rates of the hot to cold airstreams is 1.6. Using variable specific heats, determine (a) the mixture temperature at the inlet of the room and (b) the rate of heat gain of the room.
FIGURE P5–83
(a)
The mixture temperature at the inlet of the room.
Answer to Problem 83P
The mixture temperature at the inlet of the room is
Explanation of Solution
Here, the warm and cold streams of fluids are mixed in a rigid mixing chamber and operates at steady state. Hence, the inlet and exit mass flow rates are equal.
Write the energy rate balance equation for two inlet and one outlet system.
Here, the rate of heat transfer is
The system is at steady state. Hence, the rate of change in net energy of the system becomes zero.
Neglect the heat transfer, work transfer, kinetic and potential energies.
The Equation (II) reduced as follows.
Substitute
Here, the ratio of mass flow rate of hot to cold air streams is
Substitute
Refer Table A-17, “Ideal-gas properties of air”
Obtain the enthalpy
Obtain the enthalpy
Write the formula of interpolation method of two variables.
Show the temperature and enthalpy values from the Table A-17 as in below table.
S.No. | x | y |
Temperature | enthalpy | |
1 | 305 | 305.22 |
2 | 307 | ? |
3 | 310 | 310.24 |
Substitute
Thus, the enthalpy
Similarly,
Obtain the enthalpy
Conclusion:
Substitute
Refer Table A-17, “Ideal-gas properties of air”
Obtain the temperature
Show the temperature and enthalpy values from the Table A-17 as in below table.
S.No. | x | y |
Enthalpy | Temperature | |
1 | 295.17 | 295 |
2 | 296.8096 | ? |
3 | 298.18 | 298 |
Substitute
The temperature
Thus, the mixture temperature at the inlet of the room is
(b)
The rate of heat gain of the room.
Answer to Problem 83P
The rate of heat gain of the room is
Explanation of Solution
Write the formula for mass flow rate of cold air
Here, the volumetric flow rate of air is
Express the formula for heat gain by the room.
Here, the mass flow rate of mixed air entering the room is
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The gas constant of air is
Conclusion:
Substitute
Substitute
Substitute
Thus, the rate of heat gain of the room is
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Chapter 5 Solutions
Thermodynamics: An Engineering Approach
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