Theory and Analysis:
The air conditioning unit can be analyzed by breaking it down to resemble an ideal
vapor-compression refrigeration cycle. There is a condenser, evaporator and a capillary
tube that acts as the expansion valve for the system. The work input is done by the
compressor which is also in the ideal cycle, and a fan which was found to be negligible in
the results. There were some differences that the A.C unit had with respect to the ideal
cycle so it became more reasonable to model it after the actual vapor-compression
refrigeration cycle. Although the pressure drop in the pipes was taken to be negligible
there was still heat transfer from the surroundings, the refrigerant going into the
compressor was superheated, and entropy increased throughout the system. There were
basically two systems that were evaluated the air side which is an open system and the
R22 coolant side which is a closed system. The air side has mass that can be transferred
through it while the R22 side cannot.
The processes involved in the cycle were:
 Isentropic Compression from points 1-2 where it was assumed to be adiabatic.
 Constant pressure heat transfer out of the system in the piping from points 2-3.
 Adiabatic throttling process through the condenser from points 4-5 where the h
values remained constant.
 From points 5-6 there is a constant pressure heat transfer into the system through
the evaporator.
Add figure of Ideal cycle
Equations used during analysis:
1. Pressures of the room air, the evaporator exit, and compressor exit
Eqn. 1


p.gr  linterp T.satH2O p.satH2O T.dbroom


pge  linterp TsatH2O psatH2O Tdbexevp
pgc  linterp TsatH2O psatH2O Tdbexcon


For the pressure of the gas in the room was found by linear interpolating from the values
given in the air tables attached to the lab instructions. All of these pressures had to be
taken from the saturated table to get the correct values.
2. The specific humidity of the room air, evap. exit and the comp. exit are needed next to
further calculations.
Eqn. 2
pv1  room pgr
pv2  evap pge
pv3  cond pgc
The pressure of water vapor in the air can be found by using Eqn. 2 shown above. The
relative humidity was measured at the beginning of the lab and the pressure of the gas at
each point was found in Eqn. 1. Using these values for the water vapor pressure and the
Eqn. below the specific humidity can be found for each point.
Eqn. 3
p v1
proom 1
1  0.622
p v2
pexevp  2
2  0.622
p v3
pexcon  3
3  0.622
The relative humidity for each is found by using the solver in MathCad to rearrange the
above equation for w. the pressure values in the above equations were taken by
measurements while the air conditioning unit was running in steady state.
3. The enthalpy of the room can be found by using the following equation.
Eqn. 4
Tdbroom  273.15K  kJ
 Tdbroom  273.15K

h1Tdbroom 1  
 1  2501  1.805

K
K


 kg
To solve for the enthalpy of the room the dry bulb temperature for the room and the
specific humidity for the room must be known. The room dry bulb temperature was given
and the specific humidity was solved for in equation 3. This equation can be repeated for
each of the three air side points by substituting in the respective dry-bulb temperatures
and humidity.
4. In order to find the heat load into the environment there was a series of equations that
have to be used with each other.
Eqn. 5 and 6
 cont   cona  3  cona
mcon   cont vcon Acon
 evapt   evapa  2  evapa
mevap   evapt vevap Aevap
The density and the mass flowrate of the condenser and evaporator were found using
Eqn. 5 and 6. The density of both was interpolated by using the supplied tables attached
to the lab instructions and the specific humidity were found using Eqn. 3. For the mass
flowrate the velocity and area of the condenser and evaporator were measured during the
data collection.
Eqn. 7


Qevap1  mevap hexevap  hroom


Qcon1  mcon hexcon  hroom
Qtot1  Qevap1  Qcon1
The total heat flow out of the system is the sum of the heat taken in by the evaporator and
the heat expelled into the environment by the condenser. If the condenser outlet is not
vented properly the system will be counterproductive.
5. The enthalpy of the evaporators surroundings (point 4 and 6) needs to be solved for
next in order to reach the COP value.
Eqn. 8


h4  linterp TsatR22 hsat  T4


h6  linterp Tsupevap  hsupevap  T6
The value at point for is saturated and a point 6 the mixture is superheated therefore the
correct tables must be used for interpolation to get correct results. Once the values are
interpolated the work into the system must be calculated.
6. The work of the compressor and fan need to be known in order to find the mass
flowrate of R22 through the condenser.
Eqn. 9
Wcom  Ic Vs
Wfan  If  Vs
The work of the compressor is just the current going through into the compressor times
the voltage supply to the unit. Both of the values were measured in the lab so the work
can be computed directly.
Eqn. 10
mr22e 


mevap hexevap  hroom  .5Wfan
h4  h6
The above equation was found by taking an energy balance around the evaporator and
solving for the mass flowrate. The mass flowrate uses the work of the fan which was split
in half between the condenser and the evaporator, the enthalpy of the in and out flows
and the mass flowrate through the evaporator. The enthalpy from Eqn. 4 and Eqn. 8 while
the work into the system is used from Eqn. 9 to find the mass flowrate.
7. Solving for the COP of the evaporator is straight forward using values already solved
for in previous equations.
Eqn. 11
COPe 


mr22e h6  h 4
Wcom
The coefficient of performance is directly solved for using the answers found in Eqns. 810. This value is one of the rating factors for the air conditioning unit.
8. The refrigeration effect and capacitance is needed as it is the industries way of rating
their system.
Eqn. 12 and 13
kg
kJ
kJ
Qe  .01   250.748
 97.245 
EER  3.413 COPe
s 
kg
kg 
The capacitance equation used the values found in Eqn. 10 and 8. The capacitance should
be lower than the rated valued due to the lab conditions. The EER is COP times a
constant ratio that gives the industry rating of the unit. The EER found in the lab was
reasonably smaller than that provided by Panasonic.
9. Finding the entropy values for the T-s Diagram.
Eqn. 14
h4
hfg x  hf
Using the above equation to solve for the enthalpy at point 5 due to the fact that is it a
mixture with an unknown quality. Since h4=h5 Eqn. 14 can be used to find the quality.
The enthalpy of the saturated vapor and latent heat of vaporization are found from the
tables that were provided for water vapor.
Eqn. 15
s 5  s fg x5  s f
Since the quality is now known from Eqn. 14 the entropy at point 5 can be calculated by
using the above equation and the known values from the tables attached to the lab
instructions.
10. Finding the entropy at all of the remaining points to complete the T-s diagram.
Eqn. 16


s 1  linterp Tsupevap  s supevap  T1



s 4  linterp TsatR22 s r22f  T4



s 2  linterp Tsupcon  s supcon  T2

s 6  linterp Tsupevap  s supevap  T6

s 3  linterp Tsupcon  s supcon  T3
The above equations use the same type of interpolation and the enthalpy equations used
previously did. The only caution is to make sure that the correct tables for saturated and
superheated steam are used for the correct points. Once all the values are found you can
use these results and the temperatures measured to plot the Ts diagram.
Equipment, methods, procedure:
Six type K thermocouples are connected to the data acquisition system and mounted at
key points in the refrigerant piping; the evaporator outlet, the compressor inlet, the
compressor outlet, the condenser inlet, the condenser outlet, and the evaporator inlet. This
placement was predetermined for the experiment.
• Haier Model # HPAC9M Portable Air Conditioner used in this lab utilizes R22 as the
refrigerant. The specifics for this unit are in attached sheets.
• Omega RH83 Digital Sling Psychrometer/Thermo Hygrometer was used to find the
room dry bulb temperature and the relative humidity of the air surrounding the unit by
holding the unit anywhere that is reasonably far from the exit points of the unit. This
device is also used to find the dry bulb temperature and relative humidity of the
evaporator and the condenser outlet points by holding the psychrometer in front of the air
flows leaving both parts.
• FLUKE 336 Clamp Meter (Ammeter) was used to find the current flow into the
compressor by clamping around the red wire that is easiest to access behind the control
panel of the air conditioning unit.
• EXTECH Instruments Model No. 451112 Vane Anemometer used to measure the outlet
velocity from the condenser and the evaporator. This device must be held with the yellow
dot on the side with the air flow hitting it.
• Control Company Model No. 14-648-51 Aneroid Barometer used for taking the
pressure of the atmosphere in the room. Device is factory calibrated so the values can be
read directly off of the device and used in calculations with an uncertainty of .05 kpa.
• Mitutoyo Model No. CD-6”CS Digital Caliper measured the outlet areas of the
condenser and evaporator air flows. Make sure that multiple measurements are taken of
the inner diameters of the outlet ducts since they aren’t exactly circular. The uncertainty
of this device can be neglected do to the multiple measurements and averaging done in
finding the values.
• Extech Multimaster 560 digital multimeter found the wall outlet voltage that the air
conditioning unit was taking its power from. This is done by sticking the positive and
negative probes into the wall socket and reading the value from the meter.
• Two Bourdon tube pressure gauges are attached to the refrigerant piping at the
evaporator outlet and the compressor outlet. The bourdon tubes were used to measure the
evaporator and compressor outlet pressures of the R22 refrigerant. The pressure gauges
can be read with two different scales, the psi scale was used with an uncertainty of .5psi.
All measurements were taken at least twice and the average was found to minimize the
error in measurement going into the calculations. Constant pressure through the
condenser and the evaporator making the assumption of inlet and outlet pressures in the
evaporator and condenser being equal valid. The air conditioner unit must be allowed to
run until the displays are shown to be as close to steady state as possible.
Photo and Sketch Needed
Bibliography:
[1] Cengel, Yunus A., and Michael A. Boles. Thermodynamics An Engineering
Approach. 5th ed. New York, NY: McGraw Hill, 2006.
[2] Incropera, Frank P., and David P. Dewitt. Fundamentals of Heat and Mass Transfer.
5th ed. Hoboken, NJ: John Wiley & Sons, Inc. 2002.
[3] Moran, Michael J., Shapiro, Howard, N., Fundamentals of Engineering
Thermodynamics. 5th ed. Hoboken, NJ: John Wiley & Sons, Inc. 2004.
[4] 2R12S3R126A-6A. Air Conditioning Department. Panasonic Industrial Company.
Analysis of results:
All the results that were found made sense with what was known at the start of the
experiment. The rated EER for the air conditioning unit was provided as 10.75 btu/whr,
the value found in the experiment was 7.865 btu/whr. This value is lower because the
factory specifications were at certain conditions that were more ideal than that of the lab
room during the experiment. The room temperature was a lot lower at 24.4 deg. Celsius
compared to 35deg; also the evaporator and condenser temperatures were lower than the
rated ones. This difference in temperature causes the water vapors to have a higher
composition and make the efficiency of the system to decrease. The previous reason is
also a major factor to the reason why the capacity was not the 8,000 btu/hr that the
manufacturer rated the unit at instead it was -----.
Conclusion and recommendations:
All of the data collected during this experiment is enough to explain to any layman what
the air conditioning unit will do when it is put into use in the lab settings. Anyone can use
the same type of system to analyze any air conditioning unit to see what the actual output
of the unit into the surrounding environment will be instead of going by what the
optimum values are that are provided by the manufactured that are purposely skewed to
make their product sound better.
The pros of doing the lab this way was that it can be performed by anyone as long as
supporting instructions and directions are given in a clear manner. The cons of making
the lab simpler by assuming certain constant variables is that the values are as exact as
some would like them to be. For the purpose of this lab which was to show the different
effects of area, velocity, temperature, humidity, and cooling fluid on an air conditioning
system all simplifications were beneficial.
In order to get this lab to be more effective it should be in a controlled environment. The
air conditioning unit should be placed in a room with a temperature like the rated temp
and as close to ideal air conditions as possible. Also limiting the uncertainty in the
measurement devices would decrease the difference in the known values and the found
values for the unit. The measurements were taken in the positions that would account for
the right amount of heat load and enthalpy for each state that the flow goes through.
Simplifying assumptions were made during the experiment to make the data easier to
collect and analyze. The effects of the pressure loss could be analyzed but should be
small enough to wear there would be no significant difference in the values reached.
The original hypothesis that was made for the system to have slightly lower values than
that provided by Panasonic were found to be accurate with all values found to be a
reasonable amount lower than the known specifications.