Universität Duisburg-Essen 4. Semester Fakultät für Ingenieurwissenschaften, IVG April 2013 Fachgebiet Thermodynamik Dr. M. A. Siddiqi

Thermodynamics Lab

Properties of Matter: Measurement of properties of matter

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Experiment: Measurement of Properties of matter Introduction All substances have properties that we can use to identify them. There are two basic types of properties that we can associate with matter. These properties are called as physical properties and chemical properties. Properties that do not change the chem-ical nature of matter are called physical properties and the properties that do change the chem-ical nature of matter are called chemical properties. Color, smell, freezing point, boiling point, melting point, infra-red spectrum, attraction (paramagnetic) or repulsion (diamagnetic) to magnets, opacity, viscosity and density are the examples of physical properties. Heat of combustion (calorific value), reactivity with water, pH etc. are the examples of chemical properties of matter. The exact knowledge of these properties of fluids is necessary for the proper design and functioning of technical plants. The measurement of these properties is of utmost importance. Some properties of fluids which are important for process industries are: 1. Transport properties (Viscosity, Thermal conductivity, Diffusion coefficient) 2. Thermal and Calorific Properties (Specific heat capacity, Coefficient of expansion, En-

thalpy of vaporization, Calorific value (higher heating value), Lower heating value, Density, Compressibility)

In this practical the viscosity, the heating values, and the enthalpy of vaporization for a given fluid will be measured. 1. Experiment Measurement of the higher and the lower heating values for a fuel gas 1.1 Description The heating value or energy value of a substance, usually a fuel or food (see food energy), is the amount of heat released during the combustion of a specified amount of it. The energy value is a characteristic for each substance. It is measured in units of energy per unit of the substance, usually mass, such as: kJ/kg, kJ/mol. The higher heating value (HHV) (or gross energy or upper heating value or gross calorific value (GCV) or higher calorific value (HCV)) is determined by bringing all the products of combustion back to the original pre-combustion temperature, and in particular condensing any vapor produced. Such measurements often use a temperature of 25°C. This is the same as the thermodynamic enthalpy of combustion since the enthalpy change for the reaction assumes a common temperature of the compounds before and after combustion, in which case the water produced by combustion is liquid. The higher heating value takes into account the latent heat of vaporization of water in the combustion products, and is useful in calculating heating val-ues for fuels where condensation of the reaction products is practical (e.g., in a gas-fired boil-er used for space heat). In other words, HHV assumes all the water component is in liquid state at the end of combustion (in product of combustion).

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The lower heating value (LHV) (net calorific value (NCV) or lower calorific value (LCV)) is determined by subtracting the heat of vaporization of the water vapor from the higher heating value. This treats any H2O formed as a vapor. The energy required to vaporize the water therefore is not realized as heat. 2. Physical basis 2.1 Definitions: The higher heating value (Ho ) (or gross energy or upper heating value or gross calorific value (GCV) or higher calorific value (HCV)) is determined by bringing all the products of combustion back to the original pre-combustion temperature, and in particular condensing any vapor produced. Such that: a) the measurements are at a temperature of 25°C, b) the combustion products from carbon and sulphur, namely carbon dioxide and sulphur

dioxide are present as gas, c) nitrogen is not oxidised, d) the water present in the fuel (before combustion) and the water formed during the

combustion are in liquid form.

This is the same as the thermodynamic enthalpy of combustion since the enthalpy change for the reaction assumes a common temperature of the compounds before and after combustion, in which case the water produced by combustion is liquid. The higher heating value takes into account the latent heat of vaporization of water in the combustion products, and is useful in calculating heating values for fuels where condensation of the reaction products is practical (e.g., in a gas-fired boiler used for space heat). In other words, HHV assumes all the water component is in liquid state at the end of combustion (in product of combustion).

The lower heating value (Hu ) (net calorific value (NCV) or lower calorific value (LCV)) is determined by subtracting the heat of vaporization of the water vapor from the higher heating value. This treats any H2O formed as a vapor. The energy required to vaporize the water therefore is not realized as heat. In this case the conditions

a) b) and c) given above hold and d) the water present in the fuel (before combustion) and the water formed during the

combustion are in vapor form at 25 °C. Ho and Hu differ only when the water is present in the products. The difference between the two heating values depends on the chemical composition of the fuel. In the case of pure car-bon or carbon monoxide, the two heating values are almost identical. If water is present in the combustion products the lower heating value (Hu ) is lower than the higher heating value (Ho ) by the amount of the enthalpy of vaporization of water. The en-thalpy of vaporization of water at 25 °C is 2442 kJ/kg. Most applications that burn fuel pro-duce water vapor, which is unused and thus wastes its heat content. In such applications, the lower heating value Hu is the applicable measure.

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2.2 Measurement of higher (Ho) and lower (Hu) heating values Junker´s calorimeter consists of two open systems, a cold water system and a combustion gas system, which are thermally isolated from outside atmosphere. Heat transfer takes place be-tween these two (see Figure 1). The heat transfer can be written in terms of First law for stationary flow processes. Figure 1: Schematic sketch of Junker´s calorimeter 1. Law of Thermodynamics applied to stationary flow processes

−+−+−=+ )()vv(

21

122

12

21212 12zzghhmPQ t

As no technical work is done

12tP = 0. By appropriate design of inlet and outlet surface areas the condition v1 = v2 can be achieved. The change in the potential energy can be neglected. Hence for combustion gas system

)(GGG 1212 hhmQ

G−= (1)

and for cold water system

)(WWWW 1212 hhmQ −= (2)

Under the assumption that Junker´s calorimeter is adiabatic outside

.0GW 1212 =+QQ (3)

GQ12

WQ12

adiabatic

GGhm 2 WW hm 1

WW hm 2 GGhm 1

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From equations (1), (2), (3) and WOhTch

WWW+= follows for the isobaric process:

)(

WWWG 12w 12 TTcmQ −⋅⋅−= So that the higher heating value Ho for one kmol fuel gas

kmolkJ)(

G

12ww

G

120

WWG

nTTcm

nQ

H

−⋅=

−=

where Gn is the mole flow (kmol/s) of the fresh fuel gas before combustion. Under the assumtion that the fuel gas behaves as an ideal gas, the molar volume of the fresh gas can be calculated.

G

mm p

TR 1⋅=υ T1 = Temperature of fresh fuel gas

pG is the pressure of dry gas. However, the gas during its flow through the gas flow meter will be saturated with water and is, therefore, a mixture of dry fuel gas water vapor in saturated state. Hence pG is to be calcu-lated. It holds pges = pG + ps and pges = pBa + Δp so that pG = pBa + Δp - ps ps = ps (T) ≙ Saturation partial pressure of water vapor pBa ≙ Barometric pressure Δp = Pressure difference of gas from the surroundings Dividing the measured flow rate of fresh gas 1V through the molar volume mυ , gives the mole flow rate n in kmol/s

m

nυ

1V =

Lower heating value Hu The lower heating value Hu follows from the higher heating value Ho, when the enthalpy of vaporization of condensed water per kmol of fresh fuel gas is subtracted from Ho:

6

n

hmHH vKou

∆−=

kmolkJ

Km = Amount of water condensed per second vh∆ = Enthalpy of vaporization of water

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3. Experimental set up

(s. Bild 2)

Fuel gas will be drawn from the gas cylinder [Druckflasche] (16) by setting the pressure re-ducing valve [Druckminderer] (15) at the appropriate position and passed through the gas flow meter [Gaszähler] (1). At this point the gas volume and the temperature [Temperatur des Frischgases] (18) as well as the pressure difference of gas relative to atmospheric pressure (17) will be measured. During its flow through the gas flow meter the gas will be wetted by water and saturated. Then the gas passes through the pressure regulator [Druckregler] (2), which holds the pressure to a constant defined value. Ultimately it will be burnt in the com-bustion chamber of Junker´s calorimeter with the help of a burner [Brenner] (3) taking the saturated air from below from the air humidifier [Luftbefeuchter] (6). The overflow water will moisten the air humidifier. The combustion gases pass through the calorimeter, supply the heat to the cold water and flow out from the valve [Abgasstutzen] (12). Cold water flows from inlet (7) into calorimeter and takes the heat from the gas up to the outlet (8). The change in the temperature of cold water (

W1T – W1T ) will be recorded with the help of mercury ther-

mometers (10) + (11). The amount of cold water will be held constant with the help of over-flow devices [Überlaufvorrichtungen] (4) and (8) and determined by weighing. The con-densed water will be collected in a measuring cylinder to determine its amount. Three series of experiments will be performed burning each time 10 liter fuel gas. 4. Experimental procedure (siehe Bild 2) 4.1 Open the tap on the water storage tank for the cold water inlet to the calorimeter. The

water storage tank is placed at a height of 2 m from the floor for compensating (reducing) the pressure and temperature variations in the water pipe line. The two way tap [Zweiwegehahn] (9) must stay in the position „Abwasser“ stehen. (see the sketch ).

4.2 Keep the pressure 1.5- 2 bar at the pressure reducing valve [Druckmindererventil] (15)

of the fuel gas cylinder [Erdgasflasche] (16), whereby the discharge valve [Druck-mindererventil] remains closed.

4.3 Turn out the burner [Brenner] (3) at the calorimeter (Bajonet connection). The gas

should not flow through the burner to the calorimeter when the burner is not ignited. Otherwise a mixture of gas and air may build up in the calorimeter and may lead to explosion when the burner is turned on.

4.4 Carefully open the discharge valve at pressure reducing device [Druckminderer] (15), till the manometer (17) at the gas flow meter [Gasuhr] (1) shows an overpressure of about 40 mm water level above the atmosphere. This provides the required flow of about 2.2 liter/min of fuel gas in case the setting of the gas pressure regulator [Gas-druckreglers] (2) is not disturbed.

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4.5 Ignite (turn on) the burner [Brenner] (3) which is still outside the calorimeter and ad-just the flame so that it is almost colorless.

4.6 Place the ignited burner [Brenner] (3) just below the calorimeter. 4.7 It takes about 15 minutes to reach the stationary state so that the outlet temperature

(11) does not rise any more. The temperature difference between the cold water en-trance [Kühlwassereintritt] (10) and exit [Austritt] (11) should be about 10° C. This can be adjusted by regulating the flow of water at the tap [Wasserdosierhahn] (7).

The temperature of the exhaust gas [Abgastemperatur] (13) is (almost) equal to the temperature of the flowing gas air mixture (18), because the gas in the gas meter [ Zähler] is cooled by the cold water, the air due to intake of water (moisture) also cools down to cold water temperature. Thus the exhaust gas is brought to the temperature of cold water by cross flow heat exchange. The condensed water at the condenser [Kondensatabfluss] (14) up to the first experi-ment will be collected in a small pot. However, it is not used for the calculations.

4.8 Record the necessary readings and calculated vaues in the protocol while you are wait-ing:

4.8.1 Read the room temperature and the barometer reading for the pressure (Thermometer

and mercury barometer are hanging nearby on the wall). The reading of the barometer has been explained i the pressure measurement experi-ment in the 3rd semester. The supervisor may help you too. The correction of barometer reading to 0° C (KT) will be done with the help of the en-closed table. It may be necessary to interpolate. (Only the most important temperature correction will be done. After correction the values will be set accordingly, i.e. 1 mm Hg = 1 Torr).

4.8.2 Read the overpressure of gas in the gas flow meter [Gaszähler] p against the atmos-

pheric pressure at the manometer (17) and convert it in Torr. 4.8.3 Calculate the total pressure pges in gas flow meter. 4.8.4 Read the gas temperature at the Thermometer (18). Thermometer is fixed 180 ° turned.

4.8.5 The partial pressure of water vapor ps in gas mixture at the temperature

G1T can be tak-en from the enclosed table.

4.8.6 Calculate the partial pressure pG of dry gas (in Torr) and convert in N/m2. 4.8.7 Calculate the molar volume of dry gas.

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4.9 Three series of experiments will be performed. Each time 10 liter gas will be burned. Just after each experiment 10 more liter of gas will be burnt without determining the amount of cold water; that means total 60 liter gas will be burnt. The water condensed during the complete burning of 60 liter gas will be collected in a measuring flask and weighed. The higher heating value and the lower heating value will be determined at the entrance temperature of cooling water. The temperature dependence of the heating value is weak.

Note and record the mass of the empty flask in the beginning of the experiment. 1.Measurement run: The two way tap will be set on „Messen“ (see sketch) as the me-

ter of gas flow meter crosses 0-liter-mark. The cold water and the con-densed water will be collected in the respective empty flasks.

At the same time the beaker to measure the condensed water will be put under [Kon-densatabfluss] (14) and the first reading of the temperature of cooling water at the inlet and outlet will be noted. The inlet and outlet temperature will be read at the intervals for full liter gas. After the flow of 10 liter fuel gas the two way tap [Zweiwegehahn] will be set at „Abwasser“ and the collected amount of cold water and the flask weighed At the end the measuring flask for the condensed water will be changed. 1.Empty Run: In the period when the next 10 liter of gas are still burnt without any measurement steps the mean values of the inlet and outlet temperature , the amount of cooling water, the amount of condensed water and from these the higher heating value Ho can be calculated (the condensed water still being collected in another beaker). 2.Measurement Run: As the 10 liter empty run of the gas is finished the second meas-urement run is started. This is done as the first one. 2. Empty Run is made as the first empty run. Then the third measurement and empty runs are made. After the third Empty Run the condensed water measuring flask is taken away, the valve on the pressure reducing device is slowly closed. The flow of water to the stor-age tank is closed. The total amount of condensed water collected during the three measurement and three empty runs is noted.

4.10 Calculate the mean values of Ho and Hu. 4.11 Calculate the percentage deviation from the values given by the supplier.

Error: the errors in the measured values may come from: The readings at the beginning of the experiment and at the end are not recorded at proper time; Error in temperature reading; error in weighing.

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Universität Duisburg-Essen Fachbereich Maschinenbau Grundlagenpraktikum Thermodynamik

Date:____________________ Matr.-No.:_____________________

Time: ____________________ Name: ______________________

Experiment : Measurement of the higher and the lower heating values for a fuel gas

Determination of the partial pressure of dry fuel gas ptr

Roomtemperature Tu = °C

Barometerstand reading pBa = mmHg

Correction to 0 °C KT = mmHg

Corrected Barometerstand

pBa,Korr = pBa - KT

pBa,Korr =

Torr

Overpressure in gas flow meter

1mm WS = 0,074 Torr

Δp =

Δp =

mmWS

Torr

Total pressure in gas flow meter

pges. = pBa,Korr + Δp

pges. =

Torr

Temperature in gas flow meter

G1T (K) = 273.15 + G1T (°C)

G1T =

G1T =

°C

K

Saturation pressure of water vapor

at G1T

ps =

Torr

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Partial pressure of dry fuel gas pG = pges - ps 1 Torr = 133.3 2m

N

pG = Torr pG = 2m

N

Molar volume of dry fuel gas

G

1mm p

TRG

⋅=υ

⋅

=

2

1

m

][K kmol

J8315

mNp

KT

G

G

υ

kmol

3

mm

=υ

Notices e.g. Weight of empty flask

1. Measurement 2. Measurement 3. Measurement liter

W1T °C W2T °C

W1T °C W2T °C

W1T °C W2T °C

0 1 2 3 4 5 6 7 8 9 10

Mean value Thermometer error Corrected mean value mean temperature difference ΔTW = °C ΔTW = °C ΔTW = °C Mass1) Cooling water + flask kg kg kg Masse Behälter kg Cooling water amount mw = kg mw = kg mw = kg Amount of gas burnt (0.01 m3)

m

0.01nυ

= = kmol

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Higher heating valuet

ww w

o nTcmH ∆⋅⋅=

kgkJ2,4W =c

Ho =

kmol

kJ

Ho =

kmol

kJ

Ho =

kmol

kJ

Mean value of higher heating value Ho =

kmol

kJ

Total condensed water

(after 60 liter gas)

mKges. =

kg

Condensed water per Measure. (10 liter gas) mK = kg

Lower heating value

nhmHH Vk

ou∆⋅

−=

kgkJ2442v =∆h

Hu = kmol

kJ

Supplier´s value HoH HoH =

kmolkJ

Percentage deviation Ho

100oH

oHo ⋅−

HHH

%

Supplier´s value HuH HuH = kmol

kJ

Percentage deviation Hu

100H uH

uHu ⋅− HH

%

Weight of empty flask

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Saturation pressure of water vapor ps at various temperatures

T[°C]

ps [Torr]

T[°C]

ps[Torr]

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

4.60

4.94

5.30

5.69

6.10

6.53

7.00

7.50

8.02

8.57

9.17

9.79

10.46

11.16

11.91

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

12.70

13.54

14.42

15.36

16.35

17.39

18.50

19.66

20.89

22.18

23.55

24.99

26.51

28.10

29.78

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Correction of recorded barometer readings at temperature Tu [°C] to 0°C

pBa (mmHg)

Tu[°C] Barometer Reading pBa [mm Hg] 620 640 660 680 700 720 740 760 780 800

0 1 2

0.14 0.24 0.35

0.14 0.25 0.36

0.15 0.26 0.37

0.15 0.27 0.38

0.15 0.27 0.39

0.16 0.28 0.40

0.16 0.29 0.42

0.17 0.30 0.43

0.17 0.30 0.44

0.18 0.31 0.45

3 4 5

0.45 0.56 0.67

0.47 0.58 0.69

0.48 0.60 0.71

0.50 0.61 0.73

0.51 0.63 0.75

0.53 0.65 0.77

0.54 0.67 0.79

0.56 0.69 0.82

0.57 0.70 0.84

0.59 0.72 0.86

6 7 8

0.77 0.88 0.98

0.80 0.91 1.01

0.82 0.93 1.05

0.85 0.96 1.08

0.87 0.99 1.11

0.90 1.02 1.14

0.92 1.05 1.17

0.95 1.08 1.20

0.97 1.10 1.24

1.00 1.13 1.27

9 10 11

1.09 1.19 1.30

1.12 1.23 1.34

1.16 1.27 1.38

1.19 1.31 1.43

1.23 1.35 1.47

1.26 1.39 1.51

1.30 1.43 1.55

1.33 1.46 1.59

1.37 1.50 1.64

1.40 1.54 1.68

12 13 14

1.41 1.51 1.62

1.45 1.56 1.67

1.50 1.61 1.72

1.54 1.66 1.77

1.59 1.71 1.83

1.63 1.75 1.88

1.68 1.80 1.93

1.72 1.85 1.98

1.77 1.90 2.03

1.81 1.95 2.09

15 16 17

1.72 1.83 1.93

1.78 1.89 2.00

1.83 1.95 2.06

1.89 2.00 2.12

1.94 2.06 2.18

2.00 2.12 2.24

2.06 2.18 2.31

2.11 2.24 2.37

2.17 2.30 2.43

2.22 2.36 2.49

18 19 20

2.04 2.14 2.25

2.10 2.21 2.32

2.17 2.28 2.39

2.24 2.35 2.47

2.30 2.42 2.54

2.37 2.49 2.61

2.43 2.56 2.68

2.50 2.63 2.76

2.56 2.70 2.83

2.63 2.77 2.90

21 22 23

2.35 2.46 2.56

2.43 2.54 2.65

2.51 2.62 2.73

2.58 2.70 2.81

2.66 2.78 2.90

2.73 2.86 2.98

2.81 2.93 3.06

2.89 3.01 3.14

2.96 3.09 3.23

3.04 3.17 3.31

24 25 26

2.67 2.77 2.88

2.76 2.86 2.97

2.84 2.95 3.07

2.93 3.04 3.16

3.01 3.13 3.25

3.10 3.22 3.34

3.19 3.31 3.44

3.27 3.40 3.53

3.36 3.49 3.62

3.44 3.58 3.72

27 28 29

2.98 3.09 3.19

3.08 3.19 3.30

3.18 3.19 3.30

3.27 3.39 3.50

3.37 3.49 3.61

3.47 3.59 3.71

3.56 3.69 3.81

3.66 3.79 3.92

3.75 3.89 4.02

3.85 3.99 4.12

30 3.29 3.40 3.51 3.61 3.72 3.82 3.93 4.04 4.14 4.25 The correction values for KT will be subtracted from pBa.

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Experiment 2: Measurement of the enthalpy of vaporization 1. Description

The aim of this experiment is to determine the enthalpy of vaporization of distilled water with the help of the apparatus shown in Figure Bild 3. For this an energy balance across the calorimeter is to be done.

2. Physical basis

Every substance can exist in three different aggregate states (solid, liquid or gas). In which aggregate state it is depends on its thermodynamic state (p, T, V). In this experiment the heat energy involved during the change of state of water from gas (vapor) to liquid state (liquid water) will be determined. In the case of reversible and isobaric-isothermal change of state this is a defined quantity, the enthalpy of vaporization We will study an isobaric, reversible change of state from state 1 to state 3 for a station-ary flow process as shown in the T-s diagram given below (see Figure 4 [Bild 4]). This will describe the phase changes clearly. The state changes can be seen in three steps (see Bild 4).

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a) Change of state from 1 – 2″

Isobaric heat addition from the condition of superheated vapor [Überhitzter Dampf] up to the boundary line: The amount of heat transferred is displayed through the area 1 – 2″ s2″ – s1 or qü = h2″ – h1.

b) Change of state from 2″ – 2′ Isobaric heat withdrawl till the saturated vapor [Sattdampf] changes to saturated liquid [Siedendes Wasser]: This reversible change of state is not only isobaric but also iso-thermal. The amount of heat transferred is displayed by the area 2″ – 2′, -s2′ –s2″ or qverd = T(s2′ – s2″) = h2′ – h2″ in the case of isobaric process. It follows from here the definition for the enthalpy of vaporization (also called enthal-py of evaporation) Δhv = h2″ - h2′. It is the amount of heat which should be added isobarically and reversibly to produce saturated vapor from saturated liquid (boiling liquid).

c) Change of state from 2′ – 3

The heat transferred is displayed by the area 2′ – 3 – s3 – s2′ or qfl = h3 –h2′. This is also the heat which must be withdrawn from the saturated water to reach state 3.

From Bild 4 and from the knowledge about the change of states it can be said that the enthal-py of vaporization depends only on temperature and pressure. It decreases with increasing pressure and will vanish at critical point. Introducing the definition equation h = u + pυ leads to following relation Δhv= u″+ pυ″ – u′ – pυ′ = (u″ – u′) + p (υ″ – υ′) with u″ – u′ = internal energy of vaporization p (υ″ – υ′) = external energy of vaporization From this relation it becomes evident that at p and T = constant the heat added during evapo-ration is largely used to increase the internal energy. The remaining part represents the work

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required to compensate for the work due to change in volume (increase in volume) during the evaporation of water. Calculation of the enthalpy of vaporization Boundary conditions: The system can be regarded as adiabatic; an assumption which is valid if the cooling water temperature does not differ more than 5 °C from the temperature oft he surroundings. The change of state in cooling water mantel and in the glass spiral [Glaswen-del] can be described by the equations for the stationary flow process. The change of state in the experimental apparatus is shown the change of state 2″ – 3 in Fig-ure [Bild] 4. Energy balance:

WAWKKWEWsK hmhmhmhm +⋅=⋅+⋅ with

tmm

tmm W

WK

K ∆=

∆= ; Δt = Measurement time

)()()(WW 12 TTc

mmhh

mmhh W

K

WWEWA

K

WKs −⋅⋅=−⋅=−

For hs – hK one can write

( )WWWK

WKsWVKs Tc

mmTTchhhhh 12)()()( −⋅⋅

=−⋅+∆=−′+′−″

It follows then:

−−−⋅=∆ )()(

ww 12 KsK

WWv TTTT

mmch

In this relation cW is the specific heat capacity of cooling water which can be taken to be the same for isobaric and isochoric change of state. 3. Experimental set up Procedure Apparatus The set up may be divided into three groups which are marked in Figure [Bild] 3 with dashed lines. a) Boiler, which consists of a heater [Heizplatte] and a glass beaker [Glaskolben] filled

with ditilled water b) Isolated connecting tube [Rohrleitung] to calorimeter [Kalorimeter]

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c) Glass calorimeter [Kalorimeter], in which the saturated water vapor enters inside the spiral [Glaswendel] and during ist flow condensed completely. The outer of the spiral is cooled by flowing cold water stream.

Measurements: Measurement of temperature at different points with the help of mercury thermometer 1. Measurement of the temperature of saturated vapor TS

2. Measurement of the temperature of cooling water at entrance W1T

3. Measurement of the temperature of cooling water at entrance W2T

4. Measurement of the temperature of condensed water KT

5. Measurement of the temperature of surroundings TU (will also be required). Measurement of the amount of water flowing through the calorimeter 6. Mass of condensed water mK (it will be collected in a measuring cylinder and weighed) 7. Mass of cold water mW. The amount of cooling water flowing through the calorimeter mW

will be collected in a vessel and weighed. 4. Experimental Procedure Three runs for the measurement will be performed. About 5 liter of cooling water will be col-lected in each run. 1. Open the tap of the cold water storage tank. The outlet tube of the water should be put

inside the wash basin drain. Check the water level in gall beaker (3/4 full). 2. Put on the hot plate on 3 [Heizplatte (Heizstufe 3)]. 3. Note the temperature of the surroundings (room) TU (Thermometer on the wall near the

mercury barometer). 4. Wait till saturated vapor temperature TS = 100 °C is attained. 5. As the temperature TS = 100 ° C is reached regulate the amount of cooling water flow

through the tap (it may sometimes be necessary to regulate the heating [Heizstufe]), so that the surroundings temperature is almost the middle of the inlet and outlet tempera-tures of cooling water. With this the heat transfer with the surroundings will be mini-mized and adiabatic condition can be assumed.

6. 1. Run: The collection of the cooling water in the vessel and that of the condensed water

in the measuring cylinder will be started at the same time (simultaneously). The inlet and outlet temperatures (estimated up to one tenth degree), the temperature of the condensed water will be read and noted in the protocol. The temperature readings should be repeated after the collection of ca. 25 milliliter of condensed water. After about 50 milliliter con-densed water is collected the run will be stopped noting at the same time the reading of the balance for the amount of condensed water and that of cooling water. The amount of cold water (mass of cold water + vessel minus the mass of empty vessel) will be deter-mined by the other balance placed there.

7. As you wait for the 2nd Run calculate the enthalpy of vaporization from the 1st Run. If

necessary regulate the inlet and outlet temperature by varying the flow rate of cooling water.

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8. 2. and 3. Runs are performed as 1st Run. 9. After finishing the 3rd Run the heater should be switched off and the cooling water flow

stopped. 10. The percentage deviation of the three measurements from the given value of the enthalpy

of vaporization will be calculated. Sources of error: The errors in the measurements error may arise from: a) Readings of balances (for condensed water and the cold water) not taken at the same

time. b) The temperature difference between the mean temperature of cooling water and the

surroundings is large. c) Cooling of the condensed water. d) Errors in reading the temperature or balance or both.

21

Universität Duisburg-Essen Fachbereich Maschinenbau/IVG Thermodynamics Lab Date:____________________ Matr.-Nr.:_____________________ Time: ____________________ Name: ______________________ Experiment 2: Determination of the enthalpy of vaporization

Temperature of the surroundings TU = °C Temperature of saturated vapor TS = °C 1.Run 2. Run 3. Run

1. Reading:Balance condensed water kg kg kg Temperature of cold water entrance T1w and exit T2w; condensed water TK(°C)

T1w T2w TK T1w T2w TK T1w T2w TK

1. Reading

2. Reading

3. Reading

Mean value of T1w,T2w and TK

Mean Temperature difference T2w-T1w °C °C °C

2. Reading :Balance condensed water

kg kg kg

2.-1. Reading Balance condensed water mK= kg mK= kg mK= kg

Mass Cold water + Vessel kg kg kg

Mass Vessel kg Mass of cold water kg kg kg

)( 12W

WWk

TTmm

−⋅ °C

°C

°C

TS - TK °C °C °C Enthalpy of vaporization

−−−=∆ )()( 12 KSWW

K

WWv TTTT

mmch

cw=4.2 [kJ/kgK]

kgkJhv =∆

kgkJhv =∆

kgkJhv =∆

Literature value ∆ kgkJhv 2442=∆

Percentage deviation 100⋅∆

∆−∆

vH

vHv

hhh % % %

22

Experiment 3: Viscosity measurement with a Höppler viscometer 1.Brief Description The viscosity of a given oil is determined at a definite temperature with a Höppler falling ball viscometer. The viscosity is determined from the measurement of the time for the fall of a ball, the density of the fluid and the constants of the apparatus (Höppler viscometer). Since the viscosity is highly temperature dependent, its measurement is done at definite temperature and constant speed. This is done with the help of a thermostat. The viscosity is a measure of the resistance to the relative movement of adjacent layers of liquid. The falling ball Höppler viscometer is used to determine the viscosity of the resistance that a ball undergoes when it is dropped in a fluid under the influence of gravity. 2. Physical Principles To characterize the forces occurring during a flow process, we define the coefficient of dy-namic viscosity, which is mainly a temperature-dependent material quantity. The physical meaning of this material quantity is determined by the following consideration. Between two parallel plates A and B (see Figure 5) with the area A, the layer of a viscous liquid of the thickness L. Neglecting gravity, force F can be determined, which is necessary for the plate A to move with constant velocity v relative to plate B. As adhesion conditions resulting in the generation of a laminar flow of the fluid between the plates is assumed, so that the immediately adjacent liquid layers to the plates have the speed v (A) and 0 (B).

Figure 5: Determination of the viscosity The necessary force F for the mutual displacement of two layers of liquid is greater, the great-er the velocity gradient existing between them and the greater their contact surface (contact surface here = plate area). Then

dLdAF v~ ⋅

(1)

By introducing a proportionality factor it follows from (1):

dLdAF v⋅⋅=η (2)

or after being divided by the contact area A

dLdv⋅=ητ (3)

where F/A = τ the shear stress, prevailing between two adjacent layers of liquid vd /dL is the velocity η is dynamic viscosity coefficient. Substances for which the relationship between η and dv / dL is given by (3) are called "New-tonian fluids". In many cases, however, the viscosity apart from depending on the temperature also depends on the prevailing shear stress, so that equation (3) needs to be written as:

B (v=0)

A v

F

L

23

dLdT v),( ⋅= τητ (3a)

Fluids with shear stress-dependent viscosity are called "non-Newtonian" fluids. In addition to these cases, there exist also so-called plastic media that follow equation (3) or (3a) only after certain τ0 is exceeded. However, these are elastically deformed in the begin-ning following Hooke’s law. If the yield curve is a straight line passing from τ0, then one speaks of "Binghamschen media", for example toothpaste, honey. They follow the equation

)()(

1v0ττ

η−⋅=

TdLd

(4)

Frequently also encounters the plastic materials showing non - Newtonian behavior after ex-ceeding the minimum shear stress (yield point) . Then equation (4) should be written as:

)(),(

1v0ττ

τη−⋅=

TdLd

(4a)

Units of Viscosity From equation (2), dimension and unit of dynamic viscosity can be determined

smkg

smsmkg

msmm

N⋅

==⋅⋅

222 1

(5)

In practice the unit Poise (P) or Centipoise (cP) is frequently used.

smkg

scmgP

⋅=

⋅= 1,01

Kinematic Viscosity: For many technical problems, a new measure of viscosity, kinematic viscosity ν is used. It is given as dynamic viscosity divided by the density of the flowing medium.

ρην =

The unit of Kinematic viscosity is therefore

Stokess

mkgm

smkg 4

23

10==⋅⋅

Falling body viscometer: A falling ball in a liquid is subject to the gravity, buoyancy and the frictional force. While gravity and buoyancy are constant, the frictional forces grow at an increasing rate. The ball which falls is first accelerated up with the increasing speed till the frictional forces increase to such an extent that the resultant of the three forces is equal to zero (Fig. 6). Using the law of inertia it follows Weight = buoyancy + frictional force. According to Stokes, the frictional force on a ball at low Reynolds numbers is

24

Figure 6: balance of forces on the ball

,42v

Re6 2

2

KuFR rF πρ ⋅= where vrKu2vRe ⋅

=

For FR v6 ⋅⋅⋅= ηπ KuR rF

grgVF KuFFA ⋅=⋅⋅= 3

34πρρ

This will be

v634

34 33 ⋅⋅+⋅⋅⋅=⋅⋅⋅ ηπρπρπ KuFKuKKu rgrgr (8)

FE FA FR It follows for the viscosity

)(9

2 2

FKuKu

ltgr ρρη −⋅

⋅⋅⋅

=

= vda

tl (9)

Where l is the distance of fall, and t is the drop time. Since the drop distance is constant, all the variables of the first factor on the right side of the last equation can be summarized to a constant, which is characteristic of a specific ball and a particular viscosimeter. Then it follows:

)( FKue tK ρρη −⋅⋅= (10) Höppler Viscometer: In Höppler viscometer, the ball is not freely falling through the downpipe which is slightly inclined during the downward movement, but it is guided. Through this the errors due to ir-regular rolling motion of the ball can be avoided. The ball then rolls down on cycloidal path. Of course, in this case the equation (10) is no longer valid in the strict sense the viscometer is to be calibrated! This calibration is carried out by the manufacturer that indicates an empiri-cally determined ball constant Ke for each ball. With a known ball constant Ke and the meas-ured fall time t, the densities of the sphere and the liquid, the dynamic or kinematic viscosity can be determined immediately with the help of equation (10).

)( FKue tK ρρη −⋅⋅=

)1( −⋅⋅=F

Kue tK

ρρν (11)

Ball constant, ball density and density of the liquid used are already specified. , The viscosity should be in centipoise or centistokes.

FE

FA

FR

25

3. Experimental setup and measurement procedure: The experimental setup consists of the Hoppler viscometer and the thermostat. The Hoppler viscometer (Fig. 7) consists of a slanted downpipe (Fallrohr), which is surround-ed with a heatable glass coating. The possibility of an accurate temperature adjustment is nec-essary, since the viscosity strongly depends on the temperature, for example for normal en-gine oil the viscosity increases by a factor of 10 at an increase in temperature from 20 ° C to 70 ° C, so that a temperature change of 1 ° C will bring a change in viscosity of about 2% . The liquid is continuously circulated by a pump in the thermostat. The inflow into the jacket of the viscometer body is carried through the inlet port 1 and runs back through the drain port 2 in the thermostat. Heat losses through the viscometer jacket and hose lines, may give rise to a small temperature difference between the fluid temperature in the thermostat and the liquid temperature in the viscometer. The temperature can be set equal to that of the medium under investigation after setting the temperature equilibrium. Normal position of the viscometer: The locking pin 17 must fit into the stopper hole 18 of the support beam. This is also the starting position for the measurement. The thermostat (Fig. 8) consists essentially of the tank with the bath fluid, the heater, the cool-

26

ing circuit for cooling the bath liquid, the contact thermometer with relay for temperature con-trol and the circulatory pumps to promote circulation of the liquid in the viscometer. Thermo-stat and viscometers are connected via tubing for supply and removal of the bath liquid.

4. Experiment Procedure: 4.1 Check the level in the normal position of the viscometer. 4.2 Setting of 20 ° C ± 0.1 ° C (ask the instructor) in the viscometer using the thermostat by regulating the flow of water and the heating power. 4.3 The Viscometer is rotated through 180 ° and locked in place. The ball falls to its initial position.(serves the porpose of mixing of the liquid) 4.4 The body of viscometer is unlocked and rotated through 180 ° to bring it to normal posi-tion. The time for the ball between the two marks A and B is measured using a stopwatch. The falling time is determined such that in each case the placement of the ball stops on the mark. This is repeated 5 times and from these the average is calculated. 4.5 Evaluation: The basis is Eq. (11)

mFkue tK ⋅−⋅= )( ρρη tm = average measured time for the fall of ball

Fρην =

Ball constant Ke, ball density ρku and density of the liquid ρF are given and should be recorded in the protocol. The calculation of the viscosity should be in centipoise (g/m.s) or centistokes (10-6 m2/s). The percentage deviation of the manufacturer is to be determined (see protocol). Error:

27

The manufacturer's instructions state that the appliance is working to within 1% accuracy. The sources of error in the experiment are the time, temperature measurements and fluctua-tions in temperature. Other measurement methods: The various viscometers differ according to the type of flow generation, which develops in them. The different types are: Capillary viscometer (Hagen-Poisseuillsches Law), rotational viscometer (Couette flow: flow between two concentric rotating relative to each other cylin-drical surfaces) and the Falling ball viscometer. The majority of the devices used in practice are capillary viscometer. Rotational viscometers are also used for non - Newtonian fluids. All models in appropriately modified form are used as the operating devices for continuous and automatic monitoring. Universität Duisburg-Essen Fachbereich MaschinenbauGrundlagenpraktikum Thermodynamics Lab Date:____________________ Matr.-No.:_____________________ Time: ____________________ Name: ______________________ Experiment 3: Viscosity measurement with a Höppler Viscometer Bath temperature T = °C Ball density1) ρKu = kg/m3

Density of the fluid1) ρF = kg/m3 Ball constants1) Ke = m2/s3 Falling time (5 readings) t1 = s

t2 = s

t3 = s

t4 = s

t5 = s

Average tm = s Dynamic Viscosity

)( FKume ρρη −⋅= tK cP10mskg1 3=

η = η =

kg/ms cP

Kinematic Viscosity

Fρην =

cSt62

10s

m1 =

ν = ν =

m2/s cSt

Manufacturers data1) ηH = cP νH = cSt

Percentage deviation

100H ⋅−ηηη

100H ⋅

−ννν

% %

1) to be taken from the Instructor

28

Abkürzungen und Formelzeichen (Short terms and Formula) A m2 Fläche (area) c KJ/(kgK) spezifische Wärmekapazität (specific heat capacity) F N Kraft (force) g m/s2 Erdbeschleunigung (acceleration due to gravity) h kJ/kg Spezifische Enthalpie (specific enthalpy) Ho kJ/kmol oder kJ/kg Brennwert (calorific value) Hu kJ/kmol oder kJ/kg Heizwert (heating value) Ke m2/s2 Kugelkonstante (ball constant) L m Dicke einer Flüssigkeitsschicht (thickness of a layer of liquid) KT °C Temperaturkorrektur des Barometerstandes (temp. correction) lit. m3 Liter (liter) l m Fallstrecke der Kugel (fall distance of the ball) m kg/s Massenstrom (mass flow rate) n kmol Anzahl der Kilomole (kilo moles) n kmol/s Molenstrom (mole flow rate) p bar Druck (pressure) Δp bar Druckdifferenz (pressure difference) Pt kJ/s technische Leistung (technical power) q kJ/kg spezifische ausgetauschte Wärme (specific heat exchanged) Q kJ/s Wärmestrom (heat flow rate) rKu m Kugelradius (radius of the ball) r kJ/kg Verdampfungswärme (enthalpy of vaporization) Re Reynoldsche Zahl (Reynold number) Rm = 8,3153 kJ/(kmol K) allgemeine Gaskonstante (universal gas constant) s kJ/(kgK) spezifische Entropie (specific entropy) t s Zeit (time) T K;°C Temperatur (temperature) u kJ/kg spezifische innere Energie (specific internal energy) v m/s Geschwindigkeit (velocity) V m3 Volumen (volume) V m3/s Volumenstrom (volumetric flow rate)

mυ m3/kmol Molvolumen (molar volume) z m Höhenkoordinate (height coordinate) η kg/(ms) dynamische Zähigkeit (dynamic voscosity) ν m2/s kinematische Zähigkeit (kinematic viscosity) ρ kg/m3 Dichte (density) τ N/m2 Schubspannung (shear stress) τ0 N/m2 Fließgrenze (flow limit)

29

I n d i z e s (Index)

c Zenti (0,01) [centi (0.01)] untere:[subscript] A Auftrieb (impulse) Ba Barometer E Erdbeschleunigung (acceleration) F Flüssigkeit (liquid) G Gas (gas) ges gesamt (total) H Herstellerangabe (manufacturers data) K Kondensat (condensate) Korr. Korrigiert (corrected) Ku Kugel (sphere, ball) Kr kritisch (critical) m Mittelwert (außer bei vm = Molvolumen) [average value, (vm = molar volume)] W Kühlwasser (cold water) R Reibung (friction) s gesättigt (saturated) tr trocken (dry) u Umgebungszustand (surroundings) ü überhitzt (super heated) 1 Eintritt (entrance) 2 Austritt (exit) obere: (superscript) ′ Siedezustand (liquid state) ″ Sättigungszustand (vapour state)

30

L i t e r a t u r (literature) Versuch 1 Baehr, H. D. Thermodynamik, Springer Verlag, Berlin Knoche, K.F. Technische Thermodynamik, Braunschweig, Vieweg Verlag 1972 DIN 51900 Bestimmung des Brennwertes und des Heizwertes DIN 51850 Gasförmige Brennstoffe Heizwerte der Komponenten DIN 5499 Brennwert und Heizwert Versuch 2 Schaefer-Bergmann- Kliefoth Grundaufgaben des physikalischen Praktikums, Teubner Verlag Stuttgart, 1957 Ulrich Physikalisches Praktikum Giradet Verlag; Essen, 1963 Kohlrausch, F. Praktische Physik, Band I, Teubner Verlag, Stuttgart, 1960 Versuch 3 Prandtl, L. Führer durch die Strömungslehre, Vieweg Verlag, Braunschweig, 1965 Schlichting, H. Grenzschicht-Theorie, Braun-Verlag, Karlsruhe 1964 DIN 1342 Viskosität bei Newtonschen Flüssigkeiten DIN 53015 Messung der Viskosität mit dem Kugelfallviskosimeter DIN 51550 Bestimmung der Viskosität Hengstenberg Messen und Regeln in der Chemischen Technik Sturm Springer-Verlag, Berlin, 1964 Winkler