thermodynamique

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Physique Fondamentale
Thermodynamique
THERMODYNAMIQUE:
DILATATION THERMIQUE (Thermal Expansion).
 Thermal Expansion of a Solid
 Coefficient of Linear Expansion
 Dilatation Thermique Des Solides
 Coefficient De Dilatation linéaire
Method:
Steam is passed through a hollow, metal tube to increase the temperature of the tube. The side of the tube
is pressed against a special adapter pin on the Rotary Motion Sensor. As the metal tube expands, the pin
rotates the sensor and the change in length is accurately measured. In addition, the temperature of the tube
is measured real-time using a 10 K Ω thermistor directly connected to the tube. DataStudio is used to create
graphs of temperature vs. time and change in length vs. time. A graph of change in length vs. change in
temperature can also be created, the slope of which equals ΔL.
Advantage:
By using probeware to take measurements for the thermal expansion of a solid, students more clearly
understand the relationship
between change in temperature and change in length. The traditional method can lead to confusion, since
students often use a multimeter to measure the resistance of a thermistor for their calculation of
temperature change. The resistance of the thermistor actually decreases as its temperature increases;
therefore students could mistakenly believe that change in length and change in
Temperature are inversely related.
Experiment Includes:
Computer-based Thermal Expansion
Temperature Sensor
Rotary Motion Sensor
Steam Generator
Thermal Expansion Experiment
Manual DataStudio File for Thermal Expansion
Experiment DataStudio Lite Software
Scientific workshop 500 interface :
Ports: 2 Digital, 3 Analog
Connection: Serial (also USB compatible with
USB/Serial Converter)
Data logging: Collect up to 17,000 Analog (force,
voltage, etc.) data points or 7,000 Motion Sensor data
points
Portable: Built-in battery compartment
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 1
Physique Fondamentale
Thermodynamique
APPAREIL DE DILATATION THERMIQUE
(THERMAL EXPANSION APPARATUS)
Easier, More Sophisticated and More Simple, plus Sophistiqué et Plus
Accurate than Traditional Equipment Précis que L’équipement Traditionnel
Steel, Copper and Aluminum Tubes L'acier, Cuivre et Tubes Aluminiums
Included
ont Inclus
With PASCO’s Thermal Expansion Apparatus, students can accurately and easily investigate the expansion
of metals with increasing temperature.
How It Works:
Measure the length of a metal tube at room temperature. Then vary the temperature of the tube and
remeasure its length to determine the coefficient of linear expansion. The concept is simple (L = αLT).
Features:
 Built-in Dial Gauge: While some thermal expansion units only give single point readings of expansion,
the PASCO dial gauge measures continuously as the rod expands and gives an accurate measure of the
rod expansion (0.01 mm resolution).
 Built-in Thermistor: Temperature measurement is simple and accurate. Rather than measuring the
temperature of the steam or water moving through the tubes, a 100 Kthermistor is placed in direct
contact with each tube.
Equilibrium is quickly reached, and the temperature can be determined using a digital ohmmeter.
(Resistance-to-temperature conversion table is permanently affixed to the base.)
 Heat with Steam or Water: Since the fluid moves through the tube, there is no troublesome water jacket.
The fluid used may be steam or water at any temperature. Students don’t need to know the temperature
because the thermistor measures the tube temperature directly. This feature allows not only the
calculation of the coefficient of linear expansion, but also the determination of the linearity of the
relationship between ΔL and ΔT
 3 Drop-in Metal Tubes: Each tube snaps neatly onto the rigid base. The other two can be simultaneously
mounted on the base for convenient storage.
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 2
Physique Fondamentale
Thermodynamique
APPAREIL DE LA CONDUCTIVITE THERMIQUE
(THERMAL CONDUCTIVITY APPARATUS)
Measure Heat Flow Through 5
Different Materials
Constant Temperature
Differential Makes Calculations
Easy
 Easy to Use, No Mess
Mesurez le Courant de la Chaleur À
travers 5 Matières Différentes
La Différentielle de la Température
constante Rend des Calculs Facile
Facile Utiliser, Aucun Désordre
One of the most important considerations for buildings in the modern world is their ability to provide good
thermal insulation. This apparatus provides students a means of observing and quantifying heat flow across
a constant temperature differential. Students use 5 common materials as test samples— glass, wood,
polycarbonate, Masonite® and Sheetrock.
How It Works:
A block of ice is placed against one side of the test material. The other side is clamped against a steam
chamber, establishing a constant 100°C temperature differential. The rate at which the ice is converted to
water is a measure of the rate at which heat passes from the steam, through the test material and into the
ice.
Features:
 No Mess: the water from the melting ice runs off into the measuring cup — not on the lab table.
 Durable Test Materials: the wood, Masonite® and Sheetrock are covered with a thin aluminum sheet for
waterproofing and to ensure good thermal contact.
 Elevated Steam Reservoir: the hot reservoir is well above thelab table to eliminate heat damage.
Includes:
 Stand with insulating pads
 Plastic tubing for connecting steam generator
 Steam chamber
 Instruction manual and experiment guide
Recomanded:
 Ice molds (2)
Stream Generateur.
 Materials; 12.7 cm square: glass, wood,
Graduated Cylinder.
polycarbonate, Masonite, Sheetrock
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 3
Physique Fondamentale
Thermodynamique
APPAREIL DE L’EFFECACITE THERMIQUE
(THERMAL EFFICIENCY APPARATUS)
Typical Experiments:
Expériences Typique :
1. Real Efficiency vs. Temperature
Difference
2. Carnot Efficiency
3. Heat Pump Coefficient of Performance
4. Thermal Conductivity
5. Load for Optimum Performance
1. Efficacité Réel en fonction de La Différence
De Température
2. Efficacité De Carnot.
3. Coefficient de Performance de La Pompe a
Chaleur
4. Conductivité Thermique.
5. Chargez pour Performance Optimum
The Thermal Efficiency Apparatus is a real heat engine that can be used to investigate and clarify the
principles at work in Carnot’s ideal heat engine. Like Carnot’s model, it can be operated as a heat engine,
converting heat into work, or operated in reverse as a heat pump, transferring heat from a cold source to a
hot source. Results are typically accurate to better than 5%.
How it Works:
The key element is a Peltier device, a semiconductor that turns thermal energy into electrical energy. The
device is sandwiched between 2 blocks of aluminum which act as the hot and cold reservoirs (see the
diagram). One block is water-cooled using the built-in pump. The other is electrically heated. A 100
kthermistor is implanted in each block so temperatures can be measured with a digital ohmmeter. The
energy supplied to this heat engine is the electrical energy used to heat the aluminum block. The heat
engine does work by running a current through the load resistor. Both the energy in and the work out are
easily determined by measuring currents and voltages.
Then it’s simple to calculate the real efficiency of the engine (power out/power in) as a function of the
operating temperatures. By investigating other modes of operation, energy losses can be measured.
Students can use these results to determine the Carnot efficiency and to compare it with the theoretical
value for each set of operating temperatures.
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 4
Physique Fondamentale
As a Heat Engine . . .
A heat engine converts thermal energy into work.
First, heat is extracted from a hot reservoir. Part of
that heat is used to perform work, and the rest is
exhausted into a cold reservoir.
Diagram of Heat Engine Operation:
both real and Carnot efficiency can be
determined for each set of operating
temperatures
Thermodynamique
As a Heat Pump . . .
A heat pump is just a heat engine run in reverse.
Normally, heat flows from hot to cold. But a heat
pump uses work to pump heat from a cold
reservoir into a hot reservoir.
Diagram of Heat Pump Operation:
the actual coefficient of performance and the
theoretical maximum coefficient of
performance can be determined.
Recommended:
Basic Digital Multimetre (4 needed)
Triple Output Power Supply
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 5
Physique Fondamentale
Thermodynamique
LA LOIS DES GAZ PARFAIT
(Ideal Gas Law)
 Ideal Gas Law
 Boyle's Law
 Gay-Lussac's Law
 Loi des gaz idéal
 Loi de Boyle
 Loi de Gay-Lussac
The temperature, volume, and pressure of a gas are measured simultaneously to show that they
change according to the Ideal Gas Law. Two special cases of the Ideal Gas Law are also
examined: Constant volume (Gay-Lussac's Law) and constant temperature (Boyle's Law).
A syringe is used to vary the volume at constant temperature. A sphere of constant volume is
immersed in different temperature water baths to show the change in pressure.
Experiment Includes:
Ideal Gas Law Syringe
Absolute Zero Apparatus
Plastic Containers (3L, 2 pack)
Pressure Sensor
Thermistor Temperature Sensor
Pressure/Temperature Sensor
Ideal Gas Law Experiment Manual
DataStudio File for Ideal
Gas Law Experiment DataStudio Lite Software
Scientific workshop 500 interface :
Ports: 2 Digital, 3 Analog
Connection: Serial (also USB compatible with
USB/Serial Converter)
Data logging: Collect up to 17,000 Analog (force,
voltage, etc.) data points or 7,000 Motion Sensor data
points
Portable: Built-in battery compartment
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 6
Physique Fondamentale
Thermodynamique
RAPPORT SPECIFIQUE DES TEMPERATURES
(Ratio of specific Heats)
 Cp/Cv for a Gas
 Ruchhardt's Method of Measuring
the Ratio of Specific Heats
 Adiabatic Process
 Le Rapport Cp/Cv
 Méthode de Ruchhard Pour Mesurer
Le Rapport Spécifique Des Gaz
 Processe Adiabatique
In this experiment, the ratio of specific heat capacities for air is determined using Ruchhardt's Method of
measuring the period of oscillation of the piston in a cylinder filled with air.
A cylinder is filled with air and a Pressure Sensor is attached. The piston is plucked by hand and allowed to
oscillate. The oscillating pressure is recorded as a function of time and the period is determined. The ratio of
specific heat capacities is calculated using the period of oscillation, according to Ruchhardt’s method.
Advantage:
Since the oscillations are plotted, it is easy to accurately measure the period of oscillation.
Experiment Includes:
Heat Engine/Gas Law Apparatus TD-8572
Large Rod Stand ME-8735
45 cm Steel Rod ME-8736
Low Pressure Sensor CI-6534A
Ratio of Specific Heats Experiment Manual
DataStudio File for Ratio of Specific Heats
ExperimentDataStudio Lite Software
Scientific workshop 500 interface :
Ports: 2 Digital, 3 Analog
Connection: Serial (also USB compatible with
USB/Serial Converter)
Data logging: Collect up to 17,000 Analog (force,
voltage, etc.) data points or 7,000 Motion Sensor data
points
Portable: Built-in battery compartment
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 7
Physique Fondamentale
Thermodynamique
CYCLE MOTEUR THERMIQUE
(Heat Engine Cycle)




Heat Engine Efficiency
Isothermal Processes
Isobaric Processes
Ideal Gas Law




Efficacité Du Moteur Thermique
Le Processe Isothermique
Le Processe Isobarique
Loi Des Gaz Idéale
A P-V diagram is generated as a heat engine is taken through a cycle. From this diagram, the heat
added to the gas and the work done by the engine is measured to determine the efficiency of the engine.
This actual efficiency is compared to the theoretical maximum efficiency.
This heat engine consists of air inside a cylinder which expands when the attached can is immersed in hot
water. The expanding air pushes on a piston and does work by lifting a weight. The heat engine cycle is
completed by immersing the can in cold water, which returns the air pressure and volume to the starting
values.
The cycle is performed as follows:
1.
2.
3.
4.
With the can in the cold bath, the 200 g mass is placed on the platform.
The can is moved from the cold bath to the hot bath.
The 200 g mass is removed from the platform.
The can is moved from the hot bath to the cold bath.
The change in pressure is measured with a Low Pressure Sensor. The change in piston height is measured
by the attached string over the Rotary Motion Sensor pulley. The change in volume is calculated by
multiplying the change in piston height by the piston cross-sectional area.
Experiment Includes:
Heat Engine/Gas Law Apparatus
Scientific workshop 500 interface :
Large Rod Base
Slotted Mass Set
Ports: 2 Digital, 3 Analog
Plastic containers (3 L, 2 pack)
Connection: Serial (also USB compatible with
Thread 699-011
USB/Serial Converter)
90 cm Steel Rod
Data logging: Collect up to 17,000 Analog (force,
Rotary Motion Sensor
voltage, etc.) data points or 7,000 Motion Sensor data
Temperature Sensor
points
Low Pressure Sensor
Portable: Built-in battery compartment
Mass Hanger
Drilled Mass (10g)
Drilled Mass (20g)
Heat Engine Cycle Experiment Manual
DataStudio File for Heat Engine Cycle Experiment
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 8
Physique Fondamentale
Thermodynamique
LOI DES GAZ ADIABATIQUE
(ADIABATIQUE GAS LAW)
 Investigate the Compression of Gases
 Computer Monitors Temperature,
Pressure and Volume
 Measure the Work Done on a Gas
 Etude de La Compression Des Gaz
 Contrôle de Température Volume et
Pression Par Ordinateur
 Mesure De Travail fait Sur le Gaz
Adiabatic and isothermal processes are difficult for beginning physics students to understand. Adiabatic
Gas Law apparatus provides the ideal demonstration.
Accurate Data:
Pressure, volume and temperature are monitored by highly sensitive transducers with fast response times.
Transducer Features:
 Volume Transducer: A linear potential divider is mounted on the side of the piston. A 5-Volt source from
the computer is applied across the potentiometer element. The voltage from the commutator brush on the
cylinder is used to indicate the position of the piston and the volume of the confined gas
 . Pressure Sensor: A solid-state, piezoresistive device that forms part of a bridge circuit is mounted at
the base of the cylinder.
 Temperature Sensor: Mounted in the cylinder on the top of the base. The active element is fine nickel
wire with a high surface-to-mass ratio. The wire’s temperature changes rapidly as the gas compresses or
expands
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 9
Physique Fondamentale
Thermodynamique
A Versatile Lab Tool:
 Compare the final pressure and temperature: values predicted by the Adiabatic Gas Law.
 Measure the work done on the gas: compare it to the change in internal energy and the theoretical
work performed.
 Determine : the ratio of specific heats for the gas (-Cp/Cv).
 Use monatomic, diatomic and polyatomic gases: determine the effects of molecular structure on .
 Investigate isothermal compression and expansion.
Experiments:
Adiabatic Gas Law can be used with the
Science Workshop Interface.
The computer functions as a 3-channel
Storage oscilloscope, plotting graphs of
Pressure, temperature and volume as well
as integrating the area under a pressure
Versus volume curve to determine the work
done on the gas.
Includes:
 Adiabatic Gas Law Apparatus
 Instruction manual, experiment guide and the
fully documented experiment, “Measurement of
Work to Compress Gases Adiabatically” (sample
data included).
Scientific workshop 500 interface :
Ports: 2 Digital, 3 Analog
Connection: Serial (also USB compatible with
USB/Serial Converter)
Data logging: Collect up to 17,000 Analog (force,
voltage, etc.) data points or 7,000 Motion Sensor
data points
Portable: Built-in battery compartment
Recommended:
Gases: argon (monatomic), air or nitrogen
(diatomic), carbon dioxide (triatomic).
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 10
Physique Fondamentale
Thermodynamique
CAVITY RADIATION
 Thermal Radiation from Different Colored
Surfaces
 Cavity Radiation
 Radiation Thermique Pour Différentes
Couleur De Surface
 Cavity Radiation
The amounts of thermal radiation from different colored
Surfaces and a cavity, all at the same temperature, are
Compared.
An aluminum cube has sides that are black, white, polished aluminum and matte aluminum with a
hole. The cube is heated to approximately 90°C and an Infrared Light Sensor is moved across the
face with the hole in it to show that the hole emits more infrared radiation than the surrounding
surface. A Rotary Motion Sensor on a Linear Translator keeps track of the light sensor’s position
and the light intensity versus position is plotted. The scan in the visible spectrum is made with a
Light Sensor to confirm that the hole is darker than the surrounding surface.
Also, the intensity of radiation from the different colored surfaces is compared.
Advantage:
The temperature of the cavity is controlled by the 750 Interface and measured using a Thermister
Temperature Sensor, which reads in degrees rather than resistance, eliminating confusion about the
resistance decreasing as the temperature increases. The temperature is used to calculate the theoretical
wavelength of maximum intensity emitted by the cavity.
Experiment Includes:
Thermal Cavity TD-8580
Banna Plug Cord-Red (5 Pack) SE-9750
60 cm Optics Bench OS-8541
Linear Translator OS-8535
Aperture Bracket OS-8534
Light Sensor CI-6504A
Infrared Sensor CI-6628
Rotary Motion Sensor CI-6538
Thermistor Temperature Sensor CI-6527A
Power Amplifier II CI-6552A
Cavity Radiation Experiment Manual
DataStudio File for Cavity Radiation Experiment
Scientific workshop 500 interface :
Ports: 2 Digital, 3 Analog
Connection: Serial (also USB compatible with
USB/Serial Converter)
Data logging: Collect up to 17,000 Analog (force,
voltage, etc.) data points or 7,000 Motion Sensor data
points
Portable: Built-in battery compartment
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 11
Physique Fondamentale
Thermodynamique
RADIATION DE CORPS NOIR
(Blackbody Radiation).
 Blackbody Spectrum
 Peak Wavelength Versus Temperature
 Spectre Du Corps Noir
 Langueur D'onde Maximale En
Fonction De La Température
The spectrum of an incandescent light bulb
is scanned by hand using a prism
spectrophotometer, which measures relative
light intensity as a function of angle. A Broad
Spectrum Light Sensor is used with a prism
so the entire spectrum from approximately
400 nm to 2500 nm can be scanned
without the overlapping orders caused by
a grating.
The wavelengths corresponding to the angles are calculated using the equations for a prism
spectrophotometer. The relative light intensity can then be plotted as a function of wavelength as
the spectrum is scanned, resulting in the characteristic
Blackbody curve. The intensity of the light bulb is reduced, reducing the temperature, and the scan
is repeated to show how the curves nest with a shift in the peak wavelength.
The temperature of the bulb’s filament can then be measured indirectly by determining the
resistance of the bulb from the measured voltage and current. From the temperature, the
theoretical peak wavelength can be calculated and compared to the measured peak wavelength.
Experiment Includes:
Prism Spectrophotometer Kit OS-8544
Educational Spectrophotometer System OS-8539
Broad Spectrum Light Sensor CI-6630
Voltage Sensor CI-6503
Power Amplifier II CI-6552A
Replacement Bulb (10 pack) SE-8509
Banana Plug Cord-Black (5 Pack) SE-9751
Blackbody Radiation Experiment Manual
DataStudio File for Blackbody Radiation Experiment
Scientific workshop 500 interface :
Ports: 2 Digital, 3 Analog
Connection: Serial (also USB compatible with
USB/Serial Converter)
Data logging: Collect up to 17,000 Analog (force,
voltage, etc.) data points or 7,000 Motion Sensor data
points
Portable: Built-in battery compartment
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 12
Physique Fondamentale
Thermodynamique
TRANSFERT D’ENERGIE PAR FROTTEMENT
(Friction Energie Transfert)
 Conservation of Energy
 Specific Heat of a Solid
 Power and Work
 Conservation D’Energie
 La Chaleur Spécifique Des Solides
 L’Energie Et Le Travaille
This experiment is similar to a traditional mechanical equivalent of heat design; however, the
objective is somewhat different. The purpose of this experiment is to facilitate a discussion among
students about the types of energy in the system and the energy transfer which takes place
throughout the process. Students use a Force Sensor to measure the force as the hanging mass is
raised and lowered. The string connecting the sensor and the hanging mass is wrapped around a
meter cylinder (brass or aluminum) in a spiral pattern. The sliding friction between the string and
metal cylinder causes the cylinder to heat up. Each metal cylinder has a built-in thermistor which is
used to monitor the real-time temperature of the cylinder using DataStudio.
Using the equation Q = mc ΔT, the change in thermal energy can be calculated. In addition, the
string passes over the large pulley on the Rotary Motion Sensor for measurement of the string
velocity as it is pulled. A power-time graph is created, since power is simply the product of the
force and velocity. By integrating the power-time graph, the energy input can be determined.
Students then compare the energy input to the increase in thermal energy in the metal cylinder and
discuss other types of energy that are present in the system.
Experiment Includes:
Energy Transfer – Friction ET-8770
Force Sensor PS-2104
Rotary Motion Sensor PS-2120
Temperature Sensor PS-2125
Small “C” Clamp SE-7286
Hooked Mass Set SE-8759
Frictional Energy Transfer Experiment
Manual DataStudio Files for Frictional Energy Transfer
Experiment DataStudio Lite Software
Scientific workshop 500 interface :
Ports: 2 Digital, 3 Analog
Connection: Serial (also USB compatible with
USB/Serial Converter)
Data logging: Collect up to 17,000 Analog (force,
voltage, etc.) data points or 7,000 Motion Sensor data
points
Portable: Built-in battery compartment
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 13
Physique Fondamentale
Thermodynamique
TRANSFERT D’ENERGIE THERMOELECTRIQUE
Thémes:
 Fonctionnement de Pompe à chaleur et
moteur thermique
 utilisation des capteurs de tension et de courant
pour mesurer les conversions d'énergie
 Capteurs de température peut surveiller la
températures de réservoir
 Modèles un système de réfrigération
The Energy Transfer - Thermoelectric circuit board helps students better understand heat engines
and heat pumps. Using a Peltier device, cooling and heating effects can be observed and
measured using PASCO probeware. In addition, a cooling fan, heat sink and foam insulation can
be used to determine their effect on the heating and cooling of the Peltier device.
Includes:
Energy Transfer –Thermoelectric Circuit Board
Heat Sink
Foam Insulation (2)
Thermistor Temperature
Cables (2)
Short Patch Cords (8)
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 14
Physique Fondamentale
Thermodynamique
TRANSFERT D’ENERGIE HYDROELECTRIQUE
Thémes:
 Demonstrates Hydroelectric Power Generation
 Open Design Gives View of Spinning Turbine and
Water Stream
 Falling Water Lights an LED
The Hydro Accessory is used with the Energy Transfer-Generator (ET-8771) to demonstrate
how falling water generates electricity. The gravitational potential energy of the water is converted
into electrical energy as the falling water turns the turbine. The water can be supplied
using the optional Water Reservoir (ME-8594). The water that has passed through the turbine
is caught in a beaker and measured to determine the total mass that has fallen.
The water nozzle size and angle can be adjusted to optimize performance. By changing the
height of the Water Reservoir, different efficiencies are achieved.
Includes:
Turbine housing
Plastic turbine (4 cm diameter)
Water nozzles (5)
Tubing (2-meter long)
Plastic hose clamp
Screw driver for attaching
Hydro Accessory to Generator
ESLI, Tel : 021 85 60 65 Fax : 021 85 58 88 E-mail : info@esli.com.dz Site web : www.esli.com.dz
A.2. 15
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