Latent Heat of Fusion Purpose: The purpose of this experiment is to measure the Latent Heat of Fusion of a substance (water) as it undergoes a phase change and a temperature change when energy is transferred between this substance and its environment. Background: Water has a higher internal energy content than ice. When ice melts into the water, it absorbs thermal energy from its surroundings, but does not change temperature. The absorb energy enables water molecules in the crystalline form of ice to break free of the bonds that hold them together. The phase change from solid to liquid involves a transfer of thermal ener gy into the substance, but doesn't involve a temperature change from the substance. The thermal energy, DQ, depends on the mass, m, and the latent heat of fusion, Lf. If the substance changes from solid to liquid, and then the liquid undergoes a temperature change, the total amount of energy involved is the sum of the thermal energy for the phase change and the thermal energy for the temperature change. In our case with ice turning into water at 0°C and then the water warming up. D D D D Qsolid = Qphase change + Qtemperature change = mLf + mc T (equ.1) Where: m: is the mass of the solid (in our case ice) in Kg Lf: is the latent heat of fusion of water in J/Kg c: is the specific heat of water in J/Kg°C DT: is the change in Temperature of the cold water in °C The thermal energy comes from the environment that surrounds the substance. In our case the substance will be ice and the surrounding environment will be warm water. Since the total energy of the system must be conserved, then the energy gain by the ice plus the energy lost by the water must be equal to zero. That is: D D Qice + Qwater = 0 (equ.2) Where: D D Qwater = mwatercwater T (equ.3) Where: DT: is the change in Temperature of the surrounding environment (hot water) in °C In our case we do not have an ideal situation. We need to modify equation 2 to account for the heat transfer between the hot water and its container (the Aluminum calorimeter can). Therefore, equation 2 becomes: D D D Qice + Qwater + QAl = 0 (equ.3) Where: D D QAl = mAlcAl T (equ.4) Finally, the change of temperature DT for the Aluminum can and the hot water is the same and; therefore, can be factored out. Procedure: Data Studio Interface setup: *Set up the Data acquisition interface first so that you can start taken data as soon as you turn on your flame. 1. Connect the interface to the laptop using the USB cable. 2. Plug the temperature probe to channel A in the interface box. 3. Turn on the interface using the power button located in the front of the unit. Software Steps 1. Double Click the "PASCO Capstone" shortcut on the desktop to start the program. 2. Follow the procedure of the previous lab to setup the wireless temperature sensor. 3. Select Table and Graph from the center screen. 4. On the table's left column click the "Select Measurement" button. Then select "Time (s)" from the drop down menu. 5. On the table's right column click the "Select Measurement" button. Then select "Temperature (oC)" from the drop down menu. You are ready to start taking data. 6. Set both the time and temperature to 3 decimal places. 7. Click the "Record" button (big red button) on the lower left side of the screen to start collecting data. 8. Remember do not stop the interface until all the ice has melted in your can and the temperature is a far below the room temperature as it was initially above the room temperature. Equipment Setup: 1. Mass the calorimeter and record its mass. 2. Fill the calorimeter with enough water at room temperature to have about 1.0 to 1.5 cm of the sensor submerged. 3. Measure and record the mass of the calorimeter plus water. 4. Setup you apparatus as the demo in the front table. 5. Place the temperature probe inside the can. Secure the probe to the side of the can with tape such that its tip is not touching the bottom of the can. 6. Press the start button in the Pasco software. 7. The interface is going to start collecting data. 8. Record the initial value of the water temperature 9. Turn on the burner, make sure you have a blue flame. Make sure that no flames are coming from the side of the can. Keep the sensor away from the flame. 10. Start warming up the water until is 15 degrees Celsius above the initial temperature. 11. Record this temperature value. This is the initial temperature value of the water and the aluminum can (Ti). 12. Close the gas valve. 13. Wipe off any excess water on several small chunks of ice and immediately add them to the warm water in the calorimeter. Gently swirl the water in the calorimeter. You must coordinate this process one person will be in charge of closing the gas while the other will be ready to start adding the ice. 14. Carefully watch the temperature in the display table. 15. As the ice melts, dry more chunks and add them to the water, swirling the water continuously. 16. When the water temperature gets as far below room temperature as it was initially above room temperature (see value in step 8), and all the ice in the water is melted, stop adding ice. 17. Record the temperature value. This is the final temperature value of the water (Tf). 18. Press the stop button in the software interface to stop recording data. 19. Remove the Temperature Probe and then immediately measure and record the mass of the calorimeter plus water plus melted ice. Calculations: 1. Calculate the mass of the water, mw, where the mass of the water is the mass of the calorimeter plus water (step 3) minus the mass of the calorimeter (step 1). 2. Calculate the mass of the ice, mice, where the mass of the ice is the mass of the calorimeter plus water plus melted ice (step 17) minus the mass of the calorimeter plus water (step 3) 3. Use the mass of the water, mass of the ice, mass of the can, specific heat of water and aluminum, initial temperature of the hot water, and final temperature of the water to calculate the Latent Heat of Fusion of water. Remember that the initial Temperature of the ice-water is 0°C. 4. Compare your value for the Latent Heat of Fusion of water with the theoretical value of the Latent Heat of Fusion of water by calculating the percent error. 5. You are allowed up to 30% error. Constants Values needed: 1. Specific Heat of water (cw) = 4190 J/KgC° 2. Specific Heat of Aluminum (cAl) = 900 J/KgC° 3. Latent Heat of Fusion of water (Lf) = 3.33 E 5 J/Kg.