Title of the report

MAPUA INSTITUTE OF TECHNOLOGYDepartment of Physics

E301: LINEAR EXPANSION

DE GUZMAN, Anne K.2013150302 BSChE-2 Group 2PHY12L-A4

SCORE:Analysis /25Conclusion /25Presentation /10TOTAL

Engr. Ericson D. DimaunahanInstructorJuly 30, 2015

ANALYSISThe only difficulty our group encountered in the experiment was obtaining the smallest percentage error as possible. The cold temperature of the room which made the metal cool faster than it does in normal temperature was the biggest percentage error contributor. In definition, linear expansion is an object's change in length due to the increase in temperature, and in this experiment, the linear expansion coefficients of the rods used were determined. The factors that affect linear expansion were also considered as well as how it can affect the experiment.A steam generator was used to produce heat and was connected to the rods by a rubber tube. The temperature were determined by the digital multi-tester and the expansion base set with micro-meter gauge and thermistor.Initially, the metal tubes were measured initially from the inner edge pin to the inner edge of the bracket at the other edge of the tube using the meter stick. For the first trial, the aluminum tube was attached to the expansion base. The initial temperature was measured using the ohmmeter attached to the thermistor located in the center of the expansion base. The resistance measured was converted to temperature using the conversion table provided on the expansion base. The same procedure was done for the determination of coefficient of linear expansion of copper tube.TrialType of TubeTrial 1.Aluminum TubeTrial 2.Copper Tube

Initial Length of Tube, 702 mm700 mm

Initial Temperature, 24.4167 C25.08785 C

Change in Length of Tube, 1.2 mm0.86 mm

Final temperature of the Tube, thot71.08411 C79.092 C

Change in Temperature of the Tube, (thot trm)46.62241 C51.00415 C

Experimental Coefficient of Linear Expansion, experimental3.76 x 10-5 /C2.275 x 10-5/C

Actual Coefficient of Linear Expansion, actual28.80 x 10-6/C16.80 x 10-6/C

After recording the initial temperature, the dial gauge was set to zero and the rubber tube was connected to the end of the metal tube to let the water from the steam generator pass through. The expansion bases end was raised for the smooth flow of water and to avoid steam condensation. The condensed water inside the tube would absorb heat from the steam and will lead to error in temperature measurement. The steam entering the tube causes the pointer in the dial gauge to rotate in which one complete revolution is equal to 1 mm of expansion. The resistance recorded was converted and taken as the final temperature. Aluminum and copper tube have a certain initial length which was one factor in solving linear expansion coefficient. Change in length is dependent on this initial length. These two are directly proportional to each other. As the temperature of the tube changes by means of the steam generator, the tube also alters. The amount of change in temperature should be addressed. If the change in temperature was not large enough, less than 100 C, it is directly proportional to change in length (Sears, 2012).Since both aluminum and copper has less than 100 C change in temperature; 43 and 45 C, the relationship of change in temperature and length is appropriate for solving unknown value. The proportionality of the factors produces an equation: (Equation 1)

is the coefficient of linear expansion which demonstrates the change in length due to temperature change. It is the unknown value in this experiment.Rearranging the equation, coefficient of linear expansion can be solved using the equation

As seen from the table, the greater change in length obtained by the aluminum tube with the value 1.2 mm as compared with the 0.8 mm expansion of the copper tube. This coincides with the equation in which the change in length is proportional to the coefficient of linear expansion as well as the initial length and change in temperature, and in this case, greater coefficient of linear expansion lead to the greater change in length.

CONCLUSION

Thermal expansion is the tendency of an object to expand and become larger due to the increase in the objects temperature.

An objects expansion depends upon three factors. Firstly, it is proportional to the objects original length. When two objects with different initial lengths are equally heated, the object with greater initial length will have a greater increase in length compared to the shorter one. Secondly, the increase in length is proportional to the increase in the temperature the object undergoes. And lastly, the increase in length is dependent to the kind of material an object is composed of.

Based from the experiment, aluminum achieved a greater change in length than copper, this is due to its greater coefficient of expansion. Experimentally, the computed coefficients are 3.93 x 10-5 /C and 2.50 x 10-5/C for aluminum and copper respectively. In comparison with the actual coefficient value, we obtained 51.04 % error for aluminum and 35.414 % for copper. The large percent error was majorly because of the cold temperature in the classroom. As mentioned earlier, the cold temperature of the room made the metal cool faster than it does in normal temperature. Another one is the measurement of the change in length using the number of revolutions made by the dial gauge and the measurement of the temperature using the digital multi-tester. Inaccurate reading leads to high percentage error.