bte2222 thermal science lab experiments

8/2/2019 BTE2222 Thermal Science Lab Experiments

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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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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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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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18/31

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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19/31

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


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


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.


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

=


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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


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


Time (seconds) Water Temperature (oC) T (oC)

0 0

30

60

90

120

150

180210

240

270

300


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-


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


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=


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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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


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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

bte2222 thermal science lab experiments

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