Coefficient of Thermal Expansion Measurement Using Dilatometer - Coursework Example

Coefficient of Thermal Expansion Measurement using Dilatometer Summary Coefficient of thermal expansion for three metals (Aluminum, Brass, Steel) wascarried out using Dilatometer. It has been found that Aluminum has the highest CTE followed by brass and steel. Large error was encountered in readings for Aluminum. Reasons for same have been discussed separately. Table of Contents Introduction 2 Theory 2 Description of Apparatus 2 Test Procedure 3 Experimental Data 3 Graph 5 Sample Calculation for Brass 6 Sample Calculation for Steel 6 Sample Calculation for Aluminium 7 Accuracy of results 7 Conclusion 8 Introduction Objective of the subject experiment is to measure, both, graphically and numerically, coefficient of thermal expansion for three materials namely: brass, aluminium and steel using dilatometer. A comparison of the expansion coefficients will be carried out and any deviations from actual critically analyzed. Theory Coefficient of linear thermal expansion (CET), denoted by α, is indicative of how much a material will expand when heated. This expansion occurs as a result of increased vibrations of atoms owing of enhanced kinetic energy gained from the heat source. Consequently, the inter-atomic distance increases which ultimately causes the material to linearly expand. To calculate CET, displacement and temperature must be measured for the sample undergoing thermal cycle. There are three techniques to measure CET: Dilatometry, interferometry, and thermo-mechanical analysis. However, this experiment covers only Dilatometry technique only (ASM International Thermal Properties of Material, 2002) CET is given by the formula: Where CET is an inherent property of material and plays a significant role during material selection phase for fabrication jobs especially where high precision and accuracy is required over large thermal gradients. Description of Apparatus A push rod dilatometer was used in this experiment. Following are the basic parts of the apparatus: Specimen holder and push rod Furnace, Cryostat and bath Transducer (dial gage) As the specimen is heated in the furnace, the expansion of the specimen is transferred to a transducer (dial gage) which gives a value of the expansion length. Test Procedure Initial room temperature and length of the specimen was measured and noted The specimen was placed in the dilatometer ensuring that no foreign material was deposited on it The temperature sensor was placed at middle length, as close to specimen as possible without actually touching it as to avoid restriction in free movement of specimen The dial gage was set to zero. Temperature was increased at increments of 10 oC until 350 oC. Change in length of specimen against each 10 degree rise in temperature was noted and tabulated for further calculations. Experimental Data Following table outline the consolidated results of the experiment. CTE using formula has also been calculated for each reading. Sample calculations are given thereafter. A graph for Extension (mm) against Temperature (oC) has also been plotted. BRASS (To = 20 oC ; Lo = 50 mm) S. No. Temperature (T / oC) Change in Temperature (∆T = T-To) / oC Length (L / mm) Change in Length (∆L = L – Lo) mm CTE (α = ∆L /(∆T x L) (oC) 1 20 0 50.00 0.000 - 2 30 10 50.01 0.010 0.0000200 3 40 20 50.02 0.020 0.0000200 4 50 30 50.03 0.030 0.0000200 5 60 40 50.04 0.035 0.0000175 6 70 50 50.04 0.040 0.0000160 7 80 60 50.05 0.050 0.0000167 8 90 70 50.06 0.060 0.0000171 9 100 80 50.07 0.070 0.0000175 10 110 90 50.08 0.080 0.0000177 11 120 100 50.09 0.085 0.0000170 12 130 110 50.10 0.095 0.0000172 13 140 120 50.10 0.100 0.0000166 14 150 130 50.11 0.110 0.0000169 15 160 140 50.12 0.120 0.0000171 16 170 150 50.13 0.130 0.0000173 17 180 160 50.14 0.140 0.0000175 18 190 170 50.15 0.145 0.0000170 19 200 180 50.16 0.155 0.0000172 20 210 190 50.17 0.165 0.0000173 21 220 200 50.18 0.175 0.0000174 22 230 210 50.19 0.185 0.0000176 23 240 220 50.20 0.195 0.0000177 24 250 230 50.21 0.205 0.0000178 25 260 240 50.22 0.215 0.0000178 26 270 250 50.23 0.225 0.0000179 27 280 260 50.23 0.230 0.0000176 28 290 270 50.24 0.240 0.0000177 29 300 280 50.25 0.250 0.0000178 30 310 290 50.26 0.260 0.0000178 31 320 300 50.27 0.270 0.0000179 32 330 310 50.28 0.280 0.0000180 33 340 320 50.30 0.295 0.0000183 34 350 330 50.30 0.300 0.0000181 STEEL (To = 20 oC ; Lo = 50 mm) S. No. Temperature (T / oC) Change in Temperature (∆T = T-To) / oC Length (L / mm) Change in Length (∆L = L – Lo) mm CTE (α = ∆L /(∆T x L) (oC) 1 20 0 50.00 0.000 - 2 30 10 50.01 0.005 0.0000100 3 40 20 50.01 0.010 0.0000100 4 50 30 50.02 0.020 0.0000133 5 60 40 50.03 0.025 0.0000125 6 70 50 50.03 0.030 0.0000120 7 80 60 50.04 0.040 0.0000133 8 90 70 50.05 0.045 0.0000128 9 100 80 50.05 0.050 0.0000125 10 110 90 50.06 0.060 0.0000133 11 120 100 50.07 0.065 0.0000130 12 130 110 50.08 0.075 0.0000136 13 140 120 50.08 0.080 0.0000133 14 150 130 50.09 0.090 0.0000138 15 160 140 50.10 0.095 0.0000135 16 170 150 50.10 0.100 0.0000133 17 180 160 50.11 0.110 0.0000137 18 190 170 50.12 0.120 0.0000141 19 200 180 50.13 0.125 0.0000139 20 210 190 50.14 0.135 0.0000142 21 220 200 50.14 0.140 0.0000140 22 230 210 50.15 0.150 0.0000142 23 240 220 50.16 0.155 0.0000140 24 250 230 50.17 0.165 0.0000143 25 260 240 50.17 0.170 0.0000141 26 270 250 50.18 0.180 0.0000143 27 280 260 50.19 0.190 0.0000146 28 290 270 50.20 0.195 0.0000144 29 300 280 50.21 0.205 0.0000146 30 310 290 50.21 0.210 0.0000144 31 320 300 50.22 0.220 0.0000146 32 330 310 50.23 0.230 0.0000148 33 340 320 50.24 0.235 0.0000146 34 350 330 50.24 0.240 0.0000145 ALUMINIUM (To = 21 oC ; Lo = 50 mm) S. No. Temperature (T / oC) Change in Temperature (∆T = T-To) / oC Length (L / mm) Change in Length (∆L = L – Lo) mm CTE (α = ∆L /(∆T x L) (oC) 1 21 0 50.00 0.000 - 2 31 10 50.09 0.090 0.0001797 3 41 20 50.00 0.000 0.0000000 4 51 30 50.50 0.500 0.0003300 5 61 40 50.70 0.700 0.0003452 6 71 50 50.90 0.900 0.0003536 7 81 60 60.10 10.100 0.0028009 8 91 70 62.00 12.000 0.0027650 9 101 80 63.50 13.500 0.0026575 10 111 90 65.50 15.500 0.0026293 11 121 100 67.00 17.000 0.0025373 12 131 110 69.00 19.000 0.0025033 13 141 120 70.50 20.500 0.0024232 14 151 130 72.50 22.500 0.0023873 15 161 140 74.50 24.500 0.0023490 16 171 150 76.50 26.500 0.0023094 17 181 160 78.00 28.000 0.0022436 18 191 170 80.00 30.000 0.0022059 19 201 180 81.50 31.500 0.0021472 20 211 190 83.50 33.500 0.0021116 21 221 200 85.00 35.000 0.0020588 22 231 210 88.50 38.500 0.0020716 23 241 220 89.50 39.500 0.0020061 24 251 230 91.00 41.000 0.0019589 25 261 240 93.00 43.000 0.0019265 26 271 250 95.00 45.000 0.0018947 27 281 260 97.00 47.000 0.0018636 28 291 270 99.00 49.000 0.0018331 29 301 280 100.50 50.500 0.0017946 30 311 290 102.00 52.000 0.0017579 31 321 300 103.50 53.500 0.0017230 32 331 310 104.50 54.500 0.0016824 33 341 320 105.50 55.500 0.0016440 34 351 330 106.50 56.500 0.0016076 Graph Sample Calculation for Brass Using reading number 20: /oC Average CTE value for all 34 readings: 17.7 X 10-6 /oC Using Graph: Gradient: 0.0009 mm/oC /oC Sample Calculation for Steel Using reading number 20 /oC Average CTE value for all 34 readings: 13.6 X 10-6 /oC Using Graph: /oC Sample Calculation for Aluminium Using reading number 20 Average CTE value for all 34 readings: 1851.6 X 10-6 /oC Using Graph: /oC Accuracy of results A comparison of actual with experimental CTE of brass, aluminium and steel are given in table below. Actual (/oC)* Experimental (graphical) /oC Error (%) Brass 19 X 10-6 18 X 10-6 -5.2 Steel 13 X 10-6 14 X 10-6 7.7 Aluminium 24 X 10-6 3758 X 10-6 15558 * Taken from ASTM Handbook, published in 1995 Discussion on Results It is evident from the results that: 1) Per degree increase in length is greatest in Aluminium followed by brass and then steel. This is owing to large inter atomic distances created due to heating in Aluminium 2) The large error in Aluminum up to 15558% is primarily due to human error. The readings may have not been noted accurately or the decimal place not marked in correct location. Systematic error can safely be ruled out since CTE of steel and brass and within acceptable error of 5.2% and 7.7% respectively 3) The slight error can be attributed to bias in noting down the temperature reading and extension precisely at the same time. Moreover, non-uniform heating, improper contact of temperature element and creep within the specimen due to multiple thermal cycles over time may have contributed to the variance in CTE. A dial gage itself is not an accurate device and electronic stain gages for measurement of extension can give more accurate results. 4) As a better practice, multiple readings for temperature increase and then decrease should have been noted to average out possibility of human / systematic error. Conclusion The results comply with the values taken from ASTM Handbook for metals for both steel and brass. Readings for Aluminum must be verified since the large error can only be attributed to human fault. For per degree rise in temperature, aluminum expands most followed by brass and then steel. Works Cited ASM International. "Thermal Expansion, Thermal Properties of Metals (#06702G)." ASME International. Last modified 2002. Accessed 2013. http://www.asminternational.org/content/ASM/StoreFiles/ACFAAD6.pdf. ASTM. "Standard Test Method for Linear Thermal Expansion of Solid Materials With a Vitreous Silica Dilatometer (E228-95)." Last modified September 1995. Accessed December 2013. ftp://65.198.187.10/project/ASTM_pdf/7/RTIMOA__.PDF. Read More