Lab 3- Thermodynamics Wk 1&2

UIC Physics Department Physics 132 Laboratory Manual Thermodynamics of a Rubber Band Page 1 of 6 Thermodynamics of a Rubber Band Overview In this lab, you will investigate the variation of the tension of a rubber band with temperature and length. Specifically, you will use the experimental apparatus to measure the tension of a rubber band as a function of temperature at fixed length. By combining the measurements at several different fixed lengths, you will test the relationship for the tension that follows from a simplified model of rubber band (see Figure 1), 𝐹 ൌ ௞ ಳ ் ேௗ మ 𝐿 (1) where L is the length of the chain, T is the temperature, 𝑘 ஻ is Boltzmann’s constant, N is the number of links within the polymer chain, and d is the length of each link. In this model links within the polymer chain can point towards the right or towards the left, which allow us to calculate the number of microstates of the chain. This relationship is unexpected because it indicates that a rubber band shrinks, thereby increasing the tension force, as its temperature is increased. However, there is a simple qualitative explanation for this phenomenon: the greater internal energy available at higher temperatures allows the system to access more microstates, which consist of different configurations of the polymer chains. More configurations of the polymer chains become available if the effective length of the chain shrinks. The opposite extreme occurs when the polymer chain is fully stretched to its longest effective length; in that case there is only one microstate and the entropy is zero (ln 1). The expression for the tension force has two important features that can be tested with the rubber band apparatus described below. First, it shows that the tension force increases with temperature. Since the tension force at equilibrium is the force that pulls the rubber band inward on itself, an increase in the tension force shrinks the rubber band. So, a rubber band is expected to shrink as its temperature is increased. This is just the opposite of most materials. For example, you know that an ideal gas should expand as its temperature is increased. This unusual behavior exhibited by a rubber band will not be measured by observing a shrinking rubber band. Instead, you will fix the length of the rubber band, then measure the tension force F as the temperature T is varied. If Eq. (1) is correct, then F will increase as T increases. It also follows from Eq. ሺ1ሻ that 𝐹 ∝ 𝐿, which is Hooke’s law for a spring, with spring constant 𝑘 ൌ ௞ ಳ ் ேௗ మ , so Eq. ሺ1ሻ can be rewritten as ி ௅ ൌ ቀ ௞ ಳ ேௗ మ ቁ 𝑇 ൌ ሺ𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡ሻ𝑇 ሺ2ሻ The Eq. ሺ2ሻ predicts that the measured force divided by the length can be plotted versus temperature to yield a universal curve that will contain all the measurements. In this lab we will check if this is possible. The model used to derive Eq. ሺ1ሻ is a simplification for a rubber band, largely because a rubber band consists of many polymer chains which has been neglected. So, it is not clear that Eq. ሺ1ሻ will be useful. However, our procedure of hypothesizing a simplified model, then testing it, is a good example of how science is done. Figure 1. Model for a polymer chain that can be applied to a rubber band

UIC Physics Department Physics 132 Laboratory Manual Thermodynamics of a Rubber Band Page 2 of 6 Apparatus The apparatus is shown in the photo to the right. It contains a stretched rubber band mounted inside a tube. The tube can be filled with water at different temperatures and emptied; a thermometer allows you to measure the temperature of the water. The rubber band is in thermal contact with the water and can have its length adjusted. The amount that the rubber band is stretched from its original mounted length can be measured by a ruler. Finally, the force exerted by the rubber band can be measured by a force sensor mounted above the tube. You should find the following pieces of apparatus, or appropriate substitutes for them, at your lab station.  Apparatus pre-filled with 1 L of water and equipped with a rubber band, liquid thermometer, plastic funnel, set of pulleys, and Pasco force sensor.  Pasco 850 Universal Interface module connected to PC  1 L plastic beaker  250 mL plastic beaker  glass rod for stirring  white tray  brown tray  cooler with ice-water mixture  water boiler Figure 2

UIC Physics Department Physics 132 Laboratory Manual Thermodynamics of a Rubber Band Page 4 of 6 2. After recording the equilibrium temperature and tension, use the following procedure to change the rubber band temperature inside the tube: ➢ Open the valve at the bottom of the tube to empty it of water. The water should flow from the tube into the white tray. ➢ After emptying the tube, close the valve. ➢ Pour out the amount of water indicated in the “Preserve” column in Table 1 from the white tray into the 1 L beaker ሺif it says 0 mL you will not have to do anything hereሻ ➢ Get rid of the rest of the water in the white tray by putting it into the location indicated in the “Waste Area” column in Table 1 ➢ Add the amount of water indicated from the location indicated in the “Add” column in Table 1. Your 1L beaker should have 1L of water in it after doing this. ➢ Fill the tube with the water from the 1 L beaker ➢ Wait 2 minutes for equilibrium ➢ Record the equilibrium temperature and tension in Capstone Table and repeat the procedure for the next step listed in Table 1. It’s good to save the Capstone file after completing each step. When you’re done,  Check that the tube is filled with room temperature water and the force sensor should show the force value close to that was initially set up on.  Save the CapStone file in Workbook folder on the Taskbar  Make sure that the workstation is clean and ready for use by next lab section. Step # Preserve Waste Area Add 1 500 mL Water Container 500 mL from Boiler 2 500 mL Boiler 500 mL from Water Container 3 0 mL Water Container 1000 mL from Water Container 4 500 mL Water Container 500 mL from Cooler 5 0 mL Water Container 1000 mL from Cooler 6 500 mL Cooler 500 mL from Water Container 7 0 mL Water Container 1000 mL from Water Container 8 750 mL Water Container 250 mL from Boiler 9 0 mL Half to Water Container / Half to Boiler 500 mL from Boiler / 500 mL from Water Container 10 0 mL Water Container 1000 from Water Container Table 1

UIC Physics Department Physics 132 Laboratory Manual Thermodynamics of a Rubber Band Page 5 of 6 WEEK 2 Data Analysis Open a LibreOffice Calc file named RubberBandStretching-template.ods which is located in Workbook folder in the Taskbar of your lab station PC. In the main menu, click File  Save Experiment as and save the LibreOffice file in Workbook folder under new name: RubberBandStretching-“your initials”.ods by replacing “template” in the file name with your initials. This file represents the set of multiple measurements of the tension force for different lengths and temperatures collected by your section last week. Use these data to answer the following questions: Questions 1. When the rubber band is stretched the same amount ( L = constant), is the tension force proportional to temperature as predicted by Eq. (1): 𝐹 ൌ ௞ ಳ ் ேௗ మ 𝐿 ? If not, then give a few key reasons why the Eq (1) does not provide a good fit to the experimental data. What is the largest source of error in this experiment? _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ Hint: Create a scatter plot of selected data in LibreOffice Calc and add a trendline by clicking the Add Chart Element menu's Trendline command button. Try to use different trendlines and compare its correlation coefficients to prove your answer.