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Table of Contents
EXPERIMENT PAGE
Experiment 1: Vapour Pressure of Water at High Temperature 2
Experiment 2: Heat Capacity of Gases 5
Experiment 3: Joule-Thomson Effect 11
Experiment 4: Thermal and Electrical Conductivity of Metals (3) ABD + C 18
Experiment 5: Heat Pump 26
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Experiment 1 Vapour Pressure of Water at High Temperature
1. BACKGROUND
The thermal energy which must be taken up by one mole of liquid, to vaporise at constanttemperature is called the molar heat of vaporisation, .
At a given temperature there is a vapour pressure at which liquid and gaseous phase are in
equilibrium. When a liquid boils the vapour pressure is equal to the external (atmospheric)
pressure.
2. OBJECTIVE
i) To measure the vapour pressure of water as a function of temperature.
ii) To calculate the heat of vaporisation at various temperatures from the values
measured.iii) To determine boiling point at normal pressure by extrapolation.
3. EQUIPMENT
High pressure vapour unit
High conductive paste
Heating apparatus
Pipette, with rubber bulb, long
Tripod base
Bosshead
Support rod
4. PROCEDURE
i) Fill the high pressure steam unit with distilled water, with the aid of a pipette,
ensuring that there are no air bubbles in the line leading to the pressure gauge.
ii) Now carefully screw the vessel together.
iii) The unit is fastened with a bosshead and lies on the electric heater.
iv) Put the thermometer in the hole provided, which should be filled with head
conductive paste.
v) Heat the vessel until the gauge reads 2 MPa (20 bar).
vi) Now switch off the heater and record the pressure and temperature as equipmentcools down.
vii) Check the locking screws from time to time while the equipment is being heated and
cooling down and tighten them if necessary.
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5. REPORT
2
T
dT
Rp
dp
=
Where the universal gas constant, R = 8.3141molK
J
,
Assuming to be constant,
constTR
p +
=1
ln
i) From the results obtained, calculate for each set of pressure and
temperature
ii) From the results obtained, plot the graph of pln vs.T
1
iii) From the slope of the graph, calculate the value of . Then calculate the
percentage difference between the value obtained from the graph and the
values calculated earlier.
iv) By extrapolating the straight line in the lower region, determine the boiling
temperature of water at normal temperature.
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DATA COLLECTION
Heat of vaporization (water)
Pressure (Bar) (C) Molar (103 J mol-1)
20
19
18
17
16
15
14
13
12
11
10
9
87
6
5
4
3
2
1
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Experiment 2: Heat Capacity of Gases
1. BACKGROUND
The first law of thermodynamics can be illustrated particularly well with an ideal gas. This law
describes the relationship between the change in internal intrinsic energy Ui, the heat exchangedwith the surroundings Q,, and the constant-pressure changepdV.
dQ = dUi +pdV (1)
The molar heat capacity Cof a substance results from the amount of absorbed heat and the
temperature change per mole:
(2)
n = number of moles
One differentiates between the molar heat capacity at constant volume CV and the molar heatcapacity at constant pressure Cp.
According to equations (1) and (2) and under isochoric conditions (V const., dV = 0), the
following is true:
(3)
and under isobaric conditions (p = const., dp = 0):
(4)
Taking the equation of state for ideal gases into consideration:
pV= n R T (5)
it follows that the difference between Cp and CV for ideal gases is equal to the universal gas
constantR.
Cp CV =R (6)
It is obvious from equation (3) that the molar heat capacity CV is a function of the internalintrinsic energy of the gas. The internal energy can be calculated with the aid of the kinetic gas
theory from the number of degrees of freedomf:
(7)
where
kB = 1.38 10-23 J/K (Boltzmann Constant)
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NA = 6.02 1023 mol-1 (Avogadro's number)
Through substitution of
R = kBNA (8)
it follows that
(9)
and taking equation (6) into consideration:
(10)
The number of degrees of freedom of a molecule is a function of its structure. All particles have 3
degrees of translational freedom. Diatomic molecules have an additional two degrees of rotational
freedom around the principal axes of inertia. Triatomic molecules have three degrees of rotational
freedom. Air consists primarily of oxygen (approximately 20%) and nitrogen (circa 80%). As a
first approximation, the following can be assumed to be true for air:
f= 5
CV = 2.5 R
CV = 20.8 J K-1 mol-1
and
Cp = 3.5 R
Cp = 29.1 J K-1 mol-1.
2. OBJECTIVE
The experiment aims to determine the molar heat capacities of air at constant volume C v and at
constant pressure Cp.
3. EQUIPMENT
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Precision manometerBarometer/Manometer
Digital counter
Digital multimeter
Aspirator bottle (10000 ml)
Gas syringe (100 ml)
Stopcock, 1-way and 3-wayRubber stopper, d = 32/26 mm, 3 holes
Rubber stopper, d = 59.5/50.5 mm, 1 hole
Rubber tubing, d = 6 mm
Nickel electrode
Chrome-nickel wire
Push-button switch
4. PROCEDURE
Part A Determining the Constant Value Cv
iv) The setup is as shown in Figure 1.
v) To determine Cv, connect the precision manometer to the bottle with apiece of tubing. The manometer should be positioned exactly horizontally. Pressure
increase has to be read immediately after the heating process.
vi) Begin the measuring procedure by pressing the push button switch. The
measuring period should be less than a second.
vii) Take readings of the pressure (from the manometer), the current andvoltage.
viii) Remove the air from the aspirator bottle after each measurement.ix) Repeat steps iii) to v) in order to obtain 10 sets of results. Vary t within
the given range.
Part B Determining the Constant Value Cpi) The setup is as shown in Figure 2.
ii) Replace the precision manometer with two syringes which are connected to theaspirator bottle with the 3-way stopcock. One syringe is mounted horizontally, whereas
the other syringe is mounted vertically with the plunger facing downwards.
iii) The vertical plunger is rotated before each measurement in order to minimize
static friction.
iv) The air pressure is determined with help of the syringe scale. Take note of the
initial volume of the syringe before performing the experiment.
v) Begin the measuring procedure by pressing the push button switch. The
measuring period should be less than a second but longer than 300ms.vi) Take readings of the final volume (from the syringe), the current and voltage.
Take readings up to 1 decimal point if possible as the difference is too small.
vii) Remove the air from the aspirator bottle after each measurement and rotate the
vertical plunger.
viii) Repeat steps iv) to vii) in order to obtain 10 sets of results. Vary t within the range300ms to 1s.
5. REPORT
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Part A Determining the Constant Value Cv
a) Plot a graph of pressure versus time. Calculate the slope of the graph.
b) Given that, the indicator tube in the manometer has a radius of r= 2 mm and a pressure
change ofp = 0.147 hPa causes an alteration of l = 1 cm in length, calculate a.
Corresponding change in volume is given as V= a p
c) Calculate Cv.
where po = 1013 hPa
T0 = 273.2K
V0 = 22.414 l/mol
p = atmospheric pressure
Part B Determining the Constant Value Cp
a) Plot a graph of volume versus time. Calculate the slope of the graph.
b) Calculate Cp, given the following information.
where po = 1013 hPa
T0 = 273.2 KV0 = 22.414 l/mol
p = pa pkpa = atmospheric pressure in hPa
pk = pressure reduction due to weight of plunger
K
kk
F
gmp
=
Where mk= 0.1139 kg = mass of the plunger
g = acceleration of gravity
FK = 7.55 x 10-4 m2 = area of the plunger
c) Calculate R.
R = Cp Cv
d) Compare the calculated R to literature.
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DATA COLLECTION
Figure 1: Experimental setup for Part A
Figure 2: Experimental setup for Part B
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Part A Determining the Constant Value Cv
Time (ms) Pressure (Bar) Current (A) Voltage (V)
Part B Determining the Constant Value Cp
Time (ms)
Volume
Current (A) Voltage (V)Initial Final
Difference(by calculation)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.80.9
1.0
Experiment 3 Joule-Thomson Effect
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1. BACKGROUND
In real gases, the intrinsic energy U is composed of a thermokinetic content and a
potential energy content: the potential of the intermolecular forces of attraction. This is
negative and tends towards zero as the molecular distance increases. In real gases, the
intrinsic energy is therefore a function of the volume, and:
During adiabatic expansion during which also no external work is done, theoverall intrinsic energy remains unchanged, with the result that the potential energy
increases at the expense of the thermokinetic content and the gases cools.
At the throttle point, the effect named after Joule-Thomson is a quasi-stationary process.
A stationary pressure gradient p2 p1 is established at the throttle point. If external heatlosses and friction during the flow of the gas are excluded, then for the total energy H,
which consists of the intrinsic energy U and displacement pV:
In this equation, p1V1 or p2V2 is the work performed by an imaginary piston during the
flow of a small amount of gas by a change in position from position 1 to 2 or position 3 to
4 (see Figure 2). In real gases, the displacement work p1V1 does not equal the
displacement work p2V2; in this case:
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Fig. 3: Temperature differences measured at various ram pressures.
This means that, fro the molecular interaction potential, displacement work is
permanently done and removed:
The Joule-Thomson effect is described quantitatively by the coefficients
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For a change in the volume of a Van der Waals gas, the change in intrinsic energy is
and the Joule-Thomson coefficient is thus
In this equation, cp is the specific heat under constant pressure, and a and b are the Van
der Waals coefficients.
If the expansion coefficients
are inserted, then
The measurement values in Fig. 3 give the straight line gradients
and
The two temperature probes may give different absolute values for the same temperature.This is no problem, as only the temperature difference is important for the determination
Joule-Thomson coefficients.
The literature values are
at 20C and 10-5 Pa,
at 20C and 105 Pa.
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For CO2, witha = 3.60 m6/ mol2
b = 42.7 cm3/ mol
cp = 366.1 J/mol K
the Van der Waals equation gives the coefficient
For air, with
a = 1.40 m6/ mol2
b = 39.1 cm3/ mol
cp = 288.9 J/mol K
the Van der Waals equation gives the coefficient
2. OBJECTIVE
To determine the Joule-Thomson coefficient of CO2.
To determine the Joule-Thomson coefficient of N2.
3. EQUIPMENT
Joule-Thomson apparatus 1Temperature meter digital, 4-2 1Temperature probe, immers. Type 2
Rubber tubing, vacuum, i.d. 8mm 2
Hose clip f. 12-20 diameter tube 2
Reducing valve for CO2 / He 1
Reducing valve for nitrogen 1
Wrench for steel cylinders 1
Steel cylinder rack, mobile 1
Steel cylinder, CO2, 10 l, full 1
Steel cylinder, nitrogen, 10 l, full 1
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4. PROCEDURE
i) The set-up of the experiment is as in Fig 1.
ii) If necessary, screw the reducing valves onto the steel cylinders and check the
tightness of the main valves.
iii) Secure the steel cylinders in their location
iv) Attach the vacuum between the reducing valve and the Joule-Thomson apparatuswith hose tube clips.
v) On each side of the glass cylinders, introduce a temperature probe up to a few
milimetres from the frit and attach ith the union nut.
vi) Connect the temperature probe on the pressure side to inlet 1.
vii) Connect another temperature probe on the unpressurised side to inlet 2 of the
temperature measurement apparatus.
{PRINCIPLE OF THE EXPERIMENT: A stream of gas is fed to a throttling point, where
the gas (CO2 or N2 ) undergoes adiabatic expansion. The differences in temperature
established between the two sides of the throttle point are measured at various pressures
and the Joule-Thomson coefficients of the gases in question are calculated.}
Important Note:
a) The experimenting room and the experimental apparatus must be in a thermalequilibrium at the start of the measurement.
b) The experimental apparatus should be kept out of direct sunlight and othersources of heating and cooling.
c) Set the temperature measurement apparatus at temperature differencemeasurement.
d) Temperature meter should be switched on at least 30 min before performing theexperiment to avoid thermal drift.
e) Open the valves in the following order: steel cylinder valve, operating valve,reducing valve, so that an initial pressure of 100kPa is established.
f) Reduce the pressure to zero in stages, in each case reading off the temperaturedifference one minute after the particular pressure has been established.
g) For both gases, and determine the atmospheric pressure and ambient temperature.
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5. REPORT
a) Plot T versusp graph for both CO2 and N2.
b) Determine CO2 and N2 from the gradient of the graph.
c) Determine CO2 and N2 by calculation (for all available data).Use formula
d) Calculate the percentage difference.
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6. DATA COLLECTION
a) Temperature differences at various pressures for CO2:
P(bar) T1 (K) T2(K) T (K)
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.150.10
0.00
b) Temperature differences at various pressures for CO2:
P(bar) T1 (K) T2(K) T (K)
0.50
0.45
0.400.35
0.30
0.25
0.20
0.15
0.10
0.00
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Experiment 4 Thermal and Electrical Conductivity of Metals
1. BACKGROUND
If a temperature difference exists between different locations of a body, heat conductionoccurs. In this experiment there is a one-dimensional temperature gradient along a rod.
The quantity of heat dQ transported with time dt is a function of the cross-sectional area a
and the temperature gradient dT/dx perpendicular to the surface.
is the heat conductivity of the substance.
The temperature distribution in a body is generally a function of location and time and is
in accordance with the Boltzmann transport equation
(2)
Where r is the density and c is the specific heat capacity of the substance.
After a time, a steady state
is achieved if the two ends of the metal rod having a length lare maintained at constant
temperatures T1 and T2, respectively, by two heat reservoirs.
Substituting equation (3) in equation (2), the following equation is obtained:
(1)
(3)
(4)
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2. OBJECTIVE
To determine the thermal conductivity of copper and aluminium is determined in a
constant temperature gradient from the calorimetrically measured heat flow.
To test the electrical conductivity of copper and aluminium is determined, and the
Wiedmann-Franz law.
3. EQUIPMENT
Calorimeter vessel, 500 ml
Calor. vessel w. heat conduct. conn.
Heat conductivity rod, Cu
Heat conductivity rod, AlMagn. stirrer, mini, controlable
Heat conductive paste, 50 g
Gauze bag
Rheostat, 10 Ohm , 5.7 AImmers.heater, 300 W, 220-250VDC/AC
Temperature meter digital
Temperature probe, immers. type
Surface temperature probe
Stopwatch, digital, 1/100 sec.
Tripod base -PASS-
Bench clamp -PASS-
Support rod -PASS-, square, l 630 mm
Support rod -PASS-, square, l 1000 mm
Universal clamp
Right angle clamp -PASS-
Supporting block 1053105357 mmGlass beaker, short, 400 ml
Multitap transf., 14VAC/12VDC, 5ADigital multimeter
Universal measuring amplifier
Connecting cord, 500 mm, red
Connecting cord, 500 mm, blue
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4. PROCEDURE
Part A Heat Capacity of the Calorimeter
i) Weigh the lower calorimeter at room temperature
ii) Measure and record the room temperature.iii) Prepare hot water and record its temperature.
iv) Pour the hot water into the lower calorimeter.
v) Immediately take the temperature readings of the hot water in the calorimeterevery 10 seconds for 5 minutes.
vi) Reweigh the calorimeter to determine the mass of water.
Part B Ambient Heat
i) The calorimeter is then put under running tap water in order to get it back to
room temperature.
ii) The calorimeter is then filled with ice water. With the assistance of ice, obtainwater with a temperature of 0oC.
iii) When a temperature of 0oC is obtained, remove all the pieces of ice and recordthe temperature every minute for 30 minutes.
iv) Reweigh the calorimeter to determine the mass of water.
Part C Thermal Conductivity
i) The setup is as shown in Figure 1. In this experiment, the difference in
temperature between the upper and lower mediums are monitored, as well as the
temperature of the water in the lower calorimeter.
ii) The empty lower calorimeter is weighed.
iii) Fill the lower calorimeter with ice water. With the aid of ice, obtain atemperature of 0oC.
iv) When a temperature of 0oC is obtained, pour hot water in the uppercalorimeter. Ensure that the upper calorimeter is well filled with hot water.
v) Keep the temperature of water in lower calorimeter water at 0oC with thehelp of ice, until the difference in temperature between two points on the rod, is
steady.
vi) When a constant temperature gradient is obtained, remove all the ice in
the lower calorimeter and begin taking readings of the difference in temperature
and the temperature of the water in the lower calorimeter. Readings should be
taken every 30 seconds for 5 minutes.
Part D Electrical Conductivity
i) The setup is as shown in Figure 2. The metal rod in the setup isaluminium.
ii) Ensure that the voltage on the variable transformer is set to 6V.
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iii) The amplifier must be calibrated to 0 in a voltage-free state to avoid acollapse on the output voltage. Select the following amplifier settings:
Input Low Drift
Amplification 104
Time Constant 0
iv) Set the rheostat to its maximum value and slowly decrease the value
during the experiment.
v) Collect readings of current and voltage for six rheostat settings.
vi) Repeat steps i) to v) with the copper rod from the Part B.
Figure 1: Experimental Set-up for Thermal Conductivity
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Figure 2: Experimental Set-up for Electrical Conductivity
5. REPORT
Part A Heat Capacity of the Calorimeter
i) From the results obtained, plot a graph of temperature vs. time.
ii) The temperature of the mixture, m , is determined from extrapolating the plotted curve,
as sketched in figure below. The straight line parallel to temperature axis was drawn
such that the shaded parts are equal in area.
u = Temperature of the surrounding atmosphere
1 = Initial temperature
m = Temperature of mixture
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iii) Calculate the heat capacity of the calorimeter using the following equation:
RM
Mwww mcC
=
whereWc = Specific heat capacity of water
Wm = Mass of the water
W = Temperature of the hot water
M = Mixing temperature
R = Room temperature
Part B Ambient Heat
i) Calculate the addition of heat from the surroundings.
TCmcQ WW += )(
where
T = T T0T0 = Temperature at time t = 0
ii) Draw a graph of temperature vs time for the cold water.
iii) Draw a graph of heat from surroundings vs time.
iv) Calculate the slope for the graph which will give you dQ/dtambient.
Part C Thermal Conductivity
i) Calculate Q and draw the graph of Q vs t. Find the slope of this graph, which will
give youdt
dQambient.+ metal.
ii) Calculatedt
dQmetal, given that:
dt
dQmetal =
dt
dQambient.+ metal -
dt
dQambient
iii) Given the length of the rod as 31.5 cm and the area as 4.91x10-4 m2, calculate theheat conductivity of the rod, .
x
TA
dt
dQ
=
Part D Electrical Conductivity
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i) Calculate the electrical conductivity using the following equation:
ii) The Wiedmann-Franz Law is as stated below:
RA
l
=
LT=
Calculate the Lorenz number in each case.
iii) Given that the value of L is as follows, calculate the error in each case.
2
8
2
22
104.2
3 K
W
e
kL
==
k Universal gas constant = 1.38 10-23 J/Ke Elementary unit charge = 1.602 10-19 AS
DATA COLLECTION
Part A Heat Capacity of the Calorimeter
Hot water temperature before poured into calorimeter = ____________
Calorimeter Temperature (assume same to Room Temperature) = ___________
Hot Water
Time (seconds) Temperature (
o
C) Time (seconds) Temperature (
o
C)0 160
10 170
20 180
30 190
40 200
50 210
60 220
70 230
80 240
90 250
100 260
110 270120 280
130 290
140 300
150
Part B Ambient Heat
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Cold water
Time (mins) Temperature (oC) Time (mins) Temperature (oC)
0 0 16
1 17
2 18
3 19
4 20
5 21
6 22
7 23
8 24
9 25
10 26
11 27
12 28
13 29
14 3015
Part C Thermal Conductivity
Time (seconds) Water Temperature (oC) T (oC)
0 0
30
60
90
120
150
180210
240
270
300
Part D Electrical Conductivity
Aluminium
Reading Current (A) Voltage (V)
1
2
3
4
5
6
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Copper
Reading Current (A) Voltage (V)
1
2
3
4
5
6
Experiment 5 - Heat Pump
1. BACKGROUND
Pressures and temperatures in the circulation of the electrical compression heat pump aremeasured as a function of time when it is operated as a water-water heat pump. The energy
taken up and released is calculated from the heating and cooling of the two water baths.
When it is operated as an air-water heat pump, the coefficient of performance at different
vaporizer temperatures is determined.
The Mollier (h, log p) diagram, in which p is the pressure and h the specific enthalpy of the
working substance, is used to describe the cyclic process in heat technology. Fig. 1 shows an
idealised representation of the heat pump circuit. The curve running through the critical point
Kdelineates the wet vapour zone in which the liquid phase and gas phase coexist. In this zone
the isotherms run parallel to the h axis. Starting from point 1, the compressor compresses the
working substance up to point 2; in the ideal case this action proceeds without an exchange of
heat with the environment, i.e. isentropically (S= const.). On the way from point 3 useful
heat is released and the working substance condenses. Then the working substance flows
through the restrictor valve and reaches point 4. In an ideal restricting action the enthalpyremains constant. As it passes from point 4 to point 1, the working substance takes up energy
from the environment and vaporises. The specific amounts of energy q0 and q taken up andreleased per kg and the specific compressor workw required can be read off directly as line
segments on the graph.
q0 = h1h3q = h2 h3w = h2 h1
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For evaluation purposes the data for the working substance R 134a in the wet vapour zone areset out in Table 1.
Figure 1: h, logp diagram of a heat pump, ideal
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2. OBJECTIVE
i) Water heat pump: To measure pressure and temperature in the circuit and in the water
reservoirs on the condenser side and the vaporizer side alternately. To calculate energy
taken up and released, also the volume concentration in the circuit and the volumetric
efficiency of the compressor.
ii) Air-water heat pump: To measure vaporizer temperature and water bath temperature onthe condenser side under different operating conditions on the vaporizer side, ie.
Natural air, cold blower and hot blower.
iii) To determine the electric power consumed by the compressor and calculate the
coefficient of performance.
3. EQUIPMENT
Heat pump, compressor principle
Lab thermometer, -10+100C
Lab thermometer, w. stem, -10+110C
Heat conductive paste, 50 gHot-/Cold air blower, 1000 W
Stopwatch, digital, 1/100 sec
Tripod base -PASS-
Support rod -PASS-, square, l 250 mm
Universal clamp with joint
Glass beaker
Glass rod
4. PROCEDURE
Part A Water-water Heat Pump
i. Pour 4.5L of water into the two water reservoirs.
ii. Record all the initial pressures and temperatures before switching on the heat pump.
iii. Start the stopwatch at the same time the heat pump is switched on. Record the power
reading and the pressure and temperatures on both the vaporizer and condenser side
every minute for approximately 30 minutes.
Part B Air-water Heat Pump
i. Remove the water reservoir on the vaporizer side and dry the heat exchanger coils.
ii. Obtain a temperature of 20oC for the 4.5L water on the condenser side.iii. Record all the initial pressures and temperatures before switching on the heat pump.
iv. Start the stopwatch at the same time the heat pump is switched on. Record the power
reading, and the temperatures at the vaporizer outlet and condenser water
temperature, every minute for approximately 20 minutes.
v. Repeat steps ii to iv but with a hot blower and a cold blower approximately 30cm
away.
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5. REPORT
Part A Water-water Heat Pump
i) Mass of water:
a) condenser = ____________
b) vaporizer = _____________
ii) Plot a graph of temperature vs time for all inlet and outlet.
iii) Calculations at t = 10mins:
a) Vaporizer heat flow,t
mc wo
Q
=
2
b) Condenser heat flow,t
mc wQ
=
1
c) Average compressor power, P
d) Performance at the condenser side,P
Q=
e) Volume flow at the vaporizer side,31
0
hh
QvV
=
(v = specific volume of the vapour)
f) Geometrical volume flow, fVV gg =
GivenVg = 5.08 cm3
f= 1450 min-1
g) Volumetric efficiency of the compressor,gV
V=
Part B Air-water Heat Pump
i) Plot a graph of temperature versus time for all the results.
ii) Calculate the average vaporizer temperature.
iii) Calculate the condenser heat flow.
iv) Calculate the performance.v) Compare the results for all the conditions and discuss.
DATA COLLECTION
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Part A Water-water Heat Pump
Time
(min)
Power
(W)
Condenser Vaporiser
P1 1 ci co P2 2 vi vo0
1
2
3
4
5
6
7
8
9
10
11
1213
14
15
16
17
18
19
20
21
22
23
2425
26
27
28
29
30
Part B Air-water Heat Pump
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Time
(min)
Natural Air Hot Blower Cold Blower
Power
(W)1 vo
Power
(W)1 vo Power (W) 1 vo
0
1
2
3
4
5
6
7
8
9
10
11
12
1314
15
16
17
18
19
20
21
22
23
24
2526
27
28
29
30
31