Table of Contents. Experiment 1: Vapour Pressure of Water at High Temperature 2. Experiment 2: Heat Capacity of Gases 5

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1 1 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

2 2 Experiment 1 Vapour Pressure of Water at High Temperature 1. BACKGROUND Molar heat of vaporisation,λ, is the thermal energy needed to boil or to condense 1.00 mole of a substance at its boiling point 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 molar 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 equipment cools down. vii) Check the locking screws from time to time while the equipment is being heated and cooling down and tighten them if necessary.

3 3 5. REPORT From The Clausius-Clapeyron differential equation dp p Λ dt R T = 2 (Equation 1.1) where the universal gas constant, R = J K mol, Assuming Λ to be constant, integrating Equation 1.1 gives: p Λ 1 = const R T + ln (Equation 1.2) i) From the results obtained, calculate Λ for each set of pressure and temperature. (Note: You need to manipulate Equation 1.2 in order to calculate Λ. 1 ii) From the results obtained, plot the graph of ln p vs. T iii) iv) From the slope of the graph, calculate the value of Λ. Then calculate the percentage difference between the value obtained from the graph and the values calculated earlier. By extrapolating the straight line in the lower region, determine the boiling temperature of water at normal pressure.

4 4 DATA COLLECTION Heat of vaporization (water) Pressure (Bar) θ ( C) Molar Λ (10 3 J mol -1 )

5 5 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 exchanged with the surroundings Q,, and the constant-pressure change pdv. dq = dui + pdv (1) The molar heat capacity C of a substance results from the amount of absorbed heat and the temperature change per mole: n = number of moles One differentiates between the molar heat capacity at constant volume Cv and the molar heat capacity at constant pressure Cp. According to equations (1) and (2) and under isochoric conditions (V const., dv = 0), the following is true: (2) (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 constant R. Cp Cv = R (6) It is obvious from equation (3) that the molar heat capacity Cv is a function of the internal intrinsic energy of the gas. The internal energy can be calculated with the aid of the kinetic gas theory from the number of degrees of freedom f: where (7)

6 6 k B = J/K (Boltzmann Constant) N A = mol-1 (Avogadro's number) Through substitution of R = k B N A (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: and f = 5 C V = 2.5 R C V = 20.8 J K-1 mol-1 C p = 3.5 R C p = 29.1 J K-1 mol OBJECTIVE The experiment aims to determine the molar heat capacities of air at constant volume C v and at constant pressure C p.

7 7 3. EQUIPMENT Precision manometer Barometer/Manometer Digital counter Digital multimeter Aspirator bottle (10000 ml) Gas syringe (100 ml) Stopcock, 1-way and 3-way Rubber 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 C v iv) The setup is as shown in Figure 1. v) To determine C v, connect the precision manometer to the bottle with a piece 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 i.e 0 < t < 1s. vii) Take readings of the pressure (from the manometer), the current and voltage. 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 C p i) The setup is as shown in Figure 2. ii) Replace the precision manometer with two syringes which are connected to the aspirator 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 i.e. 300ms < t < 1s 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 range given.

8 8 5. REPORT Part A Determining the Constant Value C v 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 of p = hpa causes an alteration of l = 1 cm in length, calculate a. Corresponding change in volume is given as V = a p c) Calculate C v. where p o = 1013 hpa T 0 = 273.2K V 0 = l/mol p = atmospheric pressure V = 1.14L Part B Determining the Constant Value C p a) Plot a graph of volume versus time. Calculate the slope of the graph. b) Calculate C p, given the following information. where p o = 1013 hpa T 0 = K V 0 = l/mol p = p a p k p a = atmospheric pressure in hpa p k = pressure reduction due to weight of plunger p k = m k F g K Where m k = kg = mass of the plunger g = acceleration of gravity F K = 7.55 x 10-4 m 2 = area of the plunger c) Calculate R. R = Cp Cv

9 9 d) Compare the calculated R to literature. Figure 1: Experimental setup for Part A Figure 2: Experimental setup for Part B

10 10 DATA COLLECTION Part A Determining the Constant Value C v t (ms) Pressure (Bar) Current (A) Voltage (V) Part B Determining the Constant Value C p t (ms) Initial Volume Final Difference (by calculation) Current (A) Voltage (V)

11 11 Experiment 3 Joule-Thomson Effect 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, the overall 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 p 2 p 1 is established at the throttle point. If external heat losses 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, p 1 V 1 or p 2 V 2 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 p 1 V 1 does not equal the displacement work p 2 V 2 ; in this case:

12 12 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

13 13 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, c p 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 20 C and 10-5 Pa, at 20 C and 10 5 Pa.

14 14 For CO 2, with a = 3.60 m 6 / mol 2 b = 42.7 cm 3 / mol c p = J/mol K the Van der Waals equation gives the coefficient For air, with a = 1.40 m 6 / mol 2 b = 39.1 cm 3 / mol c p = J/mol K the Van der Waals equation gives the coefficient 2. OBJECTIVE To determine the Joule-Thomson coefficient of CO 2. To determine the Joule-Thomson coefficient of N EQUIPMENT Joule-Thomson apparatus 1 Temperature meter digital, Temperature probe, immers. Type 2 Rubber tubing, vacuum, i.d. 8mm 2 Hose clip f diameter tube 2 Reducing valve for CO 2 / He 1 Reducing valve for nitrogen 1 Wrench for steel cylinders 1 Steel cylinder rack, mobile 1 Steel cylinder, CO 2, 10 l, full 1 Steel cylinder, nitrogen, 10 l, full 1

15 15 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) On each side of the glass cylinders, introduce a temperature probe up to a few milimetres from the frit and attach with the union nut. v) Connect the temperature probe on the pressure side to inlet 1. vi) 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 (CO 2 or N 2 ) 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 thermal equilibrium at the start of the measurement. b) The experimental apparatus should be kept out of direct sunlight and other sources of heating and cooling. c) Set the temperature measurement apparatus at temperature difference measurement. d) Temperature meter should be switched on at least 30 min before performing the experiment 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 temperature difference one minute after the particular pressure has been established. g) For both gases, and determine the atmospheric pressure and ambient temperature.

16 16 5. REPORT a) Plot T (K) versus p (kpa) graph for both CO 2 and N 2. b) Determine µ CO2 and µ N2 from the gradient of the graph. c) Compare with literature values and calculate the percentage difference. Literature values of: µ CO2 = 1.16 x 10-5 K/Pa, at 20 C and 10-5 Pa. µ N2 = 0.23 x 10-5 K/Pa, at 20 C and 10 5 Pa.

17 17 6. DATA COLLECTION a) Temperature differences at various pressures for CO 2 : P (bar) T 1 (K) T 2 (K) T (K) b) Temperature differences at various pressures for N 2 : P (bar) T 1 (K) T 2 (K) T (K)

18 18 Experiment 4 Thermal and Electrical Conductivity of Metals 1. BACKGROUND If a temperature difference exists between different locations of a body, heat conduction occurs. 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. (1) λ 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 Where r is the density and c is the specific heat capacity of the substance. After a time, a steady state (2) (3) is achieved if the two ends of the metal rod having a length l are maintained at constant temperatures T1 and T2, respectively, by two heat reservoirs. Substituting equation (3) in equation (2), the following equation is obtained: (4)

19 19 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 Magn. stirrer, mini, controlable Heat conductive paste, 50 g Gauze bag Rheostat, 10 Ohm, 5.7 A Immers.heater, 300 W, VDC/AC Temperature meter digital Temperature probe, immers. type Surface temperature probe Stopwatch, digital, 1/100 sec. Tripod base -PASS- Bench clamp -PASS- Support rod -PASS-, square, l 630 mm Support rod -PASS-, square, l 1000 mm Universal clamp Right angle clamp -PASS- Supporting block mm Glass beaker, short, 400 ml Multitap transf., 14VAC/12VDC, 5A Digital multimeter Universal measuring amplifier Connecting cord, 500 mm, red Connecting cord, 500 mm, blue 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 calorimeter every 10 seconds for 5 minutes. vi) Reweigh the calorimeter to determine the mass of water.

20 20 Use ONLY Copper rod for Part B, C & D 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, obtain water with a temperature of 0 o C. iii) When a temperature of 0 o C is obtained, remove all the pieces of ice and record the 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 differences 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 a temperature of 0 o C. iv) When a temperature of 0 o C is obtained, pour hot water in the upper calorimeter. Ensure that the upper calorimeter is well filled with hot water. v) Keep the temperature of water in lower calorimeter water at 0 o C with the help 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. *Note: For procedure iii) and v): - Place the ice into a gauze bag provided. About ¼ of the gauze bag. - Stir the ice water constantly with a glass rod to obtain a temperature of 0 o C. Part D Electrical Conductivity (Use Copper rod) i) The setup is as shown in Figure 2. Use Copper rod for your experiment. ii) Ensure that the voltage on the variable transformer is set to 6V. iii) The amplifier must be calibrated to 0 in a voltage-free state to avoid a collapse on the output voltage. Select the following amplifier settings: Input Low Drift Amplification 10 4 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.

21 21 Figure 1: Experimental Set-up for Thermal Conductivity Figure 2: Experimental Set-up for Electrical Conductivity

22 22 5. REPORT Part A Heat Capacity of the Calorimeter i) From the results obtained, plot a graph of temperature ( C) vs. time (s). ii) Extrapolate the plotted curved for both increasing and decreasing part of the graph. iii) Draw a straight line parallel to temperature axis. Check the mid point of the line to assure the areas such as the shaded part in Figure 3 below are equal. iv) The temperature of the mixture, T m, is the point where the drawn straight line intersects with part II of the graph. T m T u T I Figure 3: Sample of plotted graph of T ( C) vs. time (s). where: T u = Temperature of the surrounding atmosphere T I = Initial temperature T m = Temperature of mixture v) Calculate the heat capacity of the calorimeter using the following equation: C = c W. m W. (T W - T M ) / (T M - T R ) where c = Specific heat capacity of water W m W = Mass of the water T W = Temperature of the hot water T M = Mixing temperature T R = Room temperature

23 23 Part B Ambient Heat i) Calculate the addition of heat from the surroundings. Q= ( cw mw + C) T where T = T T 0 T 0 = Temperature at time t = 0 ii) iii) iv) Draw a graph of temperature vs time for the cold water. Draw a graph of heat from surroundings vs time. Calculate the slope for the graph which will give you dq/dt ambient. Part C Thermal Conductivity i) Calculate Q and draw the graph of Q vs t. Find the slope of this graph, which will dq give you ambient.+ metal. dt ii) dq Calculate metal, given that: dt dq dq dq metal = ambient.+ metal - ambient dt dt dt iii) Given the length of the rod as 31.5 cm and the area as 4.91x10-4 m 2, calculate the heat conductivity of the rod, λ. dq dt T = λ A x Part D Electrical Conductivity i) Calculate the electrical conductivity using the following equation: ii) The Wiedmann-Franz Law is as stated below: l σ = A R λ = σ LT Calculate the Lorenz number in each case. iii) Given that the value of L is as follows, calculate the error in each case. π L= k WΩ = e 2 K k Universal gas constant = J/K e Elementary unit charge = AS

24 24 DATA COLLECTION Part A Heat Capacity of the Calorimeter Mass of calorimeter, kg Mass of calorimeter + water, kg Mass of water, kg Hot water temperature before poured in calorimeter, K Calorimeter temperature (assume same to Room Temperature), K Hot Water Time (seconds) Temperature ( o C) Time (seconds) Temperature ( o C)

25 25 Part B Ambient Heat Cold water Time (mins) Temperature ( o C) Time (mins) Temperature ( o C)

26 26 Part C Thermal Conductivity Time (seconds) Water Temperature ( o C) T ( o C) Part D Electrical Conductivity Copper Reading Current (A) Voltage (V)

27 27 Experiment 5 - Heat Pump 1. BACKGROUND Pressures and temperatures in the circulation of the electrical compression heat pump are measured 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 K delineates 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 enthalpy remains 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 and released per kg and the specific compressor work w required can be read off directly as line segments on the graph. q 0 = h 1 h 3 q = h 2 h 3 w = h 2 h 1 For evaluation purposes the data for the working substance R 134a in the wet vapour zone are set out in Table 1. Figure 1: h, log p diagram of a heat pump, ideal curve.

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29 29 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 on the 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, C Lab thermometer, w. stem, C Heat conductive paste, 50 g Hot-/Cold air blower, 1000 W Stopwatch, digital, 1/100 sec Tripod base -PASS- Support rod -PASS-, square, l 250 mm Universal clamp with joint Glass beaker Glass rod 4. PROCEDURE Part A Water-water Heat Pump i. Pour 4.5L of water into the two water reservoirs. ii. Record all the initial pressures and temperatures before switching on the heat pump. iii. Start the stopwatch at the same time the heat pump is switched on. Record the power reading and the pressure and temperatures on both the vaporizer and condenser side every minute for approximately 30 minutes. Part B Air-water Heat Pump i. Remove the water reservoir on the vaporizer side and dry the heat exchanger coils. ii. Obtain a temperature of 20 o C 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.

30 30 5. REPORT Part A Water-water Heat Pump i) Mass of water: a) condenser = b) vaporizer = ii) iii) Plot a graph of temperature vs time for all inlet and outlet. Calculations at t = 10mins: θ a) Vaporizer heat flow, Q& = c mw 2 o t θ b) Condenser heat flow, Q& = c mw 1 t c) Average compressor power, P Q d) Performance at the condenser side, ε = & P e) Volume flow at the vaporizer side, Q& 0 V& = v h h 1 3 (v = specific volume of the vapour) f) Geometrical volume flow, V& = V f Given Vg = 5.08 cm 3 f = 1450 min -1 g) Volumetric efficiency of the compressor, λ = Part B Air-water Heat Pump g g V & V g 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.

31 31 DATA COLLECTION Part A Water-water Heat Pump Time Condenser Vaporiser Power (W) (min) P 1 θ 1 θc i θc o P 2 θ 2 θv i θv o

32 32 Part B Air-water Heat Pump Time (min) Power (W) Natural Air Hot Blower Cold Blower θ 1 θv o Power (W) θ 1 θv o Power (W) θ 1 θv o