Thermal expansion of liquids TEP Related Topics Linear expansion, volume expansion of liquids, thermal capacity, lattice potential, equilibrium spacing, Grüneisen equation. Prinicple The volume expansion of liquids is determined as a function of temperature. Equipment 1 Immersion thermostat Alpha A, 230 V 08493-93 1 Bath for thermostat, Makrolon 08487-02 1 Lab thermometer,-10..+100c 38056 1 Syringe 1ml, Luer, 10 pcs 02593-03 1 Cannula 0.6x60 mm, Luer, 20 pcs 02599-04 2 Measuring tube,l.300mm,igj19/26 03024 1 Wash bottle, plastic, 250 ml 33930 2 Flask,flat bottom, 100ml,IGJ19/26 35811-01 1 Glass beaker DURAN, tall, 100 ml 36002 1 Ethyl acetate 250 ml 30075-25 1 Glycerol 250 ml 30084-25 1 Olive oil,pure 100 ml 30177-10 1 Set of Precision Balance Sartorius CPA 423S and software, 230 V 49223-88 Duration: approx. 10 minutes for set-up and 20 minutes for each tube Fig 1: P2310300 www.phywe.com P2310300 PHYWE Systeme GmbH & Co. KG All rights reserved 1
TEP Thermal expansion of liquids Tasks Determine the volume expansion of n-heptane (C 7 H 16 ), olive oil and water as a function of temperature, using the pycnometer. Set-up Set up the equipment as seen in Fig 1 (without pycnometer). Please refer to the manual of the thermostat for its installation and handling. The pycnometer is build from the flask and the measuring tube. Fig 2: Procedure. Procedure Calibration At the beginning the pycnometer must be calibrated, i.e. the relationship between the scale of the measurement tube and the volume must be determined. Assemble the pycnometer using the flask and the measurement tube. Place the empty pycnometer on the balance and set the balance to zero (Tara function). Now fill the pycnometer with water until the scale of the measurement tube is reached and measure the mass. Increase the water amount in steps of approximately 50 scale parts and measure the mass for each step. Note the results. Measurement Fill one of the three pycnometers with water, one with olive oil and one with heptane. Place one bottle in the bath and note the initial Volume V 0 and temperature T 0. Now heat up the temperature bath and note the volume at five temperature steps of 5 C each. Note the results. 2 PHYWE Systeme GmbH & Co. KG All rights reserved P2310300
Thermal expansion of liquids TEP Theory and evaluation An increase in temperature T causes the vibrational amplitude of the atoms in the crystal lattice of the solid to increase. The potential curve (Fig. 3) of the bonding forces corresponds only to a first approximation to the parabola of a harmonic oscillation (dotted line); generally it is flatter in the case of large interatomic distances than in the case of small ones. If the vibrational amplitude is large, the centre of oscillation thus moves to larger interatomic distances. The average spacing between the atoms increases, as well as the total volume V (at constant pressure p). Fig. 3: Potential curve as a function of the interatomic spacing r. α = 1 V V T P (1) is called the volume expansion coefficient; if we consider one dimension only, we obtain the coefficient of linear expansion α 1 = 1 l l T P (2) where l is the total length of the body. A rise in the temperature causes a greater thermal agitation of the molecules in a liquid and therefore an increase in its volume (water between 0 and 4 C is an exception to this, however). The coefficient of expansion of olive oil and water depends on temperature. Measured values at 20 C are: liquid α/10 3 K 1 Water 0.20 Glycerol 0.50 Olive oil 0.72 Methylated spirit 1.11 Ethyl acetate 1.37 www.phywe.com P2310300 PHYWE Systeme GmbH & Co. KG All rights reserved 3
TEP Thermal expansion of liquids Evaluation and Sample results Calibration First calculate the volume out of the mass by dividing the mass by the specific density of water. Select the right density from Table 1. Table 1: Calibration of the pycnometer Scale Mass in g Volume in cm 3 9 132.7 133.0 77 133.6 133.9 122 134.1 134.4 177 134.8 135.1 226 135.4 135.7 266 135.9 136.2 Temperature in C Density in g/cm 3 20 0,9982 25 0,9971 30 0,9956 Plot the volume versus the scale. Fit a linear function for a later calculation of the volume out of the scale. Calibration function (in this case!): V = 0.0124 cm 3 Scaleparts + 133 cm 3 35 0,9940 Table 1: Density of water in dependence of the temperature Fig. 2: Calibration of the pycnometer 4 PHYWE Systeme GmbH & Co. KG All rights reserved P2310300
Thermal expansion of liquids TEP Measurement Calculate T - T 0 for each liquid and transform the volumes from Scale parts into cm 3 using the calibration function. Water Olive oil Heptane T in C V in Scale parts T in C V in Scale parts T in C V in Scale parts T 0 = 27 V 0 = 2 T 0 = 20 V 0 = 8 T 0 = 22 V 0 = 12 32 8 25 14 27 25 37 14 30 27 32 67 42 34 35 48 37 124 47 52 40 76 42 187 52 73 45 107 47 254 Table 3: Expansion of the liquids Liquid Water Olive oil Heptane T - T 0 in C Volume in cm 3 Volume in cm 3 Volume in cm 3 0 133.02 133.10 133.15 5 133.10 133.17 133.31 10 133.17 133.33 133.83 15 133.42 133.60 134.54 20 133.64 133.94 135.32 25 133.91 134.33 136.15 Table 4: Expansion of the liquids Fig. 3 shows the thermal expansion of the liquids. The lines are straight fits to the data for calculation of the increment. Get the increment for the data. For this neglect the first two measurement points, because the heating is inhomogeneous during the beginning of the measurement. According to the theory α = 1 V T is valid. Therefore you have to divide the increment by the starting Volume V 0. V 0 Water Olive oil Heptane Increment in cm 3 /K 0.0484 0.0664 0.155 V 0 133.02 133.10 133.15 α in 10 3 /K 0.4 0.5 1.2 Theory 0.2 0.7 1.3 Table 5: Coefficients of linear expansion www.phywe.com P2310300 PHYWE Systeme GmbH & Co. KG All rights reserved 5
TEP Thermal expansion of liquids Fig. 3: Thermal expansion of the liquids (triangle up: heptane, circle: olive oil, triangle down: water) Please note, that the theoretical values are for the standard temperature T = 20 C. Note The Grüneisen equation Where α C P = γ κ V κ = 1 V V p T (5) is the compressibility and C P = U T P is the thermal capacity of the solid (U = internal energy), signifies a relationship between the mechanical and thermal properties of a solid. The Grüneisen parameter γ is defined by the change in the frequency υ of lattice vibration with volume: Δυ υ = γ ΔV V and can be calculated from macroscopic quantities in accordance with (5). 6 PHYWE Systeme GmbH & Co. KG All rights reserved P2310300