PHY12L - E301 - LINEAR EXPANSION

ANALYSIS ON LINEAR EXPANSION

 

          Linear expansion is change in length due to change in temperature. In the experiment we are required to determine the coefficient of linear expansion of metal tube namely aluminum and copper.

          The materials used in conducting the experiment are the two metal tubes (1) aluminum and (2) copper, meter stick, digital multi-tester, expansion base set with micro-meter gauge and thermistor, lastly, the steam generator with rubber tubing.   

          At first, we measured the metal tubes, aluminum and copper with an initial length of 753mm and 752 mm. After measuring the initial length of the aluminum and copper, we started to do the experiment. We produced heat in the form of steam using the steam generator that will enter the system of the tube to know the expansion rate of the metal tube.

 

         

We measure the resistance of the metal using the thermistor and attached it to the metal tube. The thermistor will determine the resistance of the metal tube. We obtain the resistance of the aluminum tube of 93, 000 ohms and copper tube of 89, 800 ohms. Every corresponding resistance has a corresponding temperature that can be seen in the expansion base. The temperature of the aluminum is 26 °C and 27 °C respectively.

 

          After recording the resistance of the metal tube, we set the dial gauge reading to zero and started to let the water in the steam generator boil and produce steam. Attaching the rubber tube in the steam generator to the one end of the tube, steam may flow from it to the metal tube. Steam passes on the system and heat the system. After some time the resistance decreases from 93, 000 ohms to 11, 440 ohms for aluminum and 89, 800 ohms to 10, 300 ohms for copper. The corresponding temperature of the resistance after heat is applied is 78°C for aluminum and 81 °C for copper. I found out that when the resistance decreases the temperature increases. It is because the intermolecular forces of attraction of the molecules want to collide because of the heat making a discrepancy of the resistance.

          Because heat is applied, the metal tube expands at a negligible change in length. The change in length for aluminum is 1.15 mm and 0.84 mm for copper. It is because of the expansion rate of the metal, the coefficient linear expansion of aluminum is greater than copper.

          We get the change in temperature by difference of the final from the initial temperature. And the change in temperature will be 52°C for aluminum and 54°C for copper.

          To check if the experiment was successful, we must solve for the experimental value of coefficient of linear expansion for both aluminum and copper. Solving for each coefficient of linear expansion, we just input the achieved data in the formula:

For the aluminum:

 

For the copper:

         

          By this time, we both have the experimental and actual values of coefficient of linear expansion.We determine the percentage error using:

 

          The error for aluminum is 23.402% and 23.128% for copper. The possible sources of errors that affect the experiment can be the following reason.

i.)                Measurement of the aluminum and copper tube using the meter stick since the measurements must be exact to the nearest millimeter.

 

ii.)              The room temperature: The room temperature affects the computed value by means where the experiment is held, since we are performing in the laboratory with an air conditioned room, we must make the experiment fast as we could. The cold temperature inside the room makes the metal cool faster than normal temperature.

 

iii.)           The materials inside the metal tube also affect the experiment. Materials inside the tube also contract or absorb heat that the steam generator releases. Like the water that remain inside the metal tube when conducting another trial, water is liquid and liquid expand more faster than the solid metal that affect the expansion of solid.

 

iv.)           Wrong measurement of the expansion base built-in gauge. When the gauge stopped moving, that is the time to record the expansion. Wrong measurement will create error.

 

v.)              If the computed water was not drained from the expansion tube, the result would be different because the condensed water inside the tube would absorb heat from the steam. When there is no condensation inside the pipe, steam energy will not be subject to heat reduction.

 

 

 

CONCLUSION ON LINEAR EXPANSION

 

          In physics, thermal expansion is the tendency of matter to increase in volume or pressure when heated. As a result of the experiment, I found out that materials having a change in temperature will have a change in dimension or length. The expansion of a material also depends on the value of its coefficient of linear expansion, the higher the coefficient of linear expansion the more it will expand. Therefore, they are directly proportional to one another.

 

          Based on the results achieved, aluminum has greater change in length than that of the copper. So therefore, we can conclude that an object with greater coefficient of linear expansion will most probably have the greater change in length. As said in the previous statement, the coefficient of linear expansion is directly proportional to change of length of a material.

There are three factors that mainly affect the change in length of a material in thermal expansion.  These are (1) the coefficient of linear expansion, (2) initial length of the body and (3) the change in the temperature.  All these three factors are directly proportional to the change in length of the material.  If these three factors increase, the change in length will also increase.  And also, some factors may lead in causing error in the experiment.

Likewise to the experiment, I found out that many things around us have something to do with thermal expansion. This experiment acquires basic knowledge and ideas about its pros and cons in everyday life. Like the roads, and train railing. They were given a space for expansion, so we can see the roads have a small slit to prevent bulky of the material or damage to the material.