213_Lab 2-Fall2021

©University of Illinois at Urbana-Champaign Physics 213 Lab 2 Summer 2023 Edition Page 1 of 14 Physics 213 --- Lab # 2 Thermal Properties of Materials (Using the new PasPort Sensors) Name: ____________________________________________ Lab Partner(s): __________________________________________________ _________________________________________________ _________________________________________________ Section: __________________ TA: _____________________________ Lab Date: _______________________________ Key Concepts In This Lab:  Temperature  Thermal Equilibrium  Heat Energy: Heat Capacity / Specific Heat  Thermal Conductivity P: /5 L: /15 T: /20

©University of Illinois at Urbana-Champaign Physics 213 Lab 2 Summer 2023 Edition Page 2 of 14 SETUP (The following will be needed for Experiment 1): 1. Make a room temperature bath. Fill the small glass beaker with water from the container marked “room temperature water” near the sink – do not use water directly from the faucet! Set the glass beaker on your table. EXPERIMENT # 1 Systems in Thermal Equilibrium In this experiment, we will compare the temperature of different systems that are in thermal equilibrium. 1. Connect the Absolute Pressure/Temperature Sensor (the same one you used in Lab 1) to PasPort 1 of the PASCO box. Make sure the temperature sensor is plugged into the pressure sensor. 2. Open the file: “ P213-Lab2_Experiment 1 - PasPort Sensors.cap ” . 3. A digital readout, table, and graph plot has been created. 4. Locate the brass cylinder and the wood block. Place them next to the room temperature bath.

©University of Illinois at Urbana-Champaign Physics 213 Lab 2 Summer 2023 Edition Page 4 of 14 9. Delete the data for this run by clicking on the “Delete Last Run” button. 10. Insert the temperature sensor into the hole in the brass cylinder, start the data acquisition system, click on the “Record” button, take temperature vs. time data, again wait long enough to attain thermal equilibrium, repeat the above analysis procedure, and record the mean and standard deviation of the equilibrium temperature of the brass cylinder in the table below. 11. Delete the data for this run by clicking on the “Delete Last Run” button. 12. Insert the temperature sensor into the hole in the wood block, start the data acquisition system, click on the “Record” button, take temperature vs. time data, again wait long enough to attain thermal equilibrium, repeat the above analysis procedure and record the mean and the standard deviation of the equilibrium temperature of the wood block in the table below. System Temperature ( o C) Air  Water Bath  Brass Cylinder  Wood Block  Questions: How do your experimental results compare with your predictions? If all of these systems are in thermal equilibrium, they should have the same temperature. Do they? Are these systems actually in thermal equilibrium with each other? If so, why do these different materials feel so different to your touch? If they are not in thermal equilibrium with each other, explain why. ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ TA Check #1

©University of Illinois at Urbana-Champaign Physics 213 Lab 2 Summer 2023 Edition Page 5 of 14 13. When completed with Experiment 1, delete the data for this run by clicking on the “Delete Last Run” button. 14. Close the file. DO NOT SAVE THE FILE!!! Then carefully remove the Absolute Pressure/Temperature sensor from PasPort 1 of the PASCO box. ****************************************************************************** Notice: The rest of the experiments today use a different temperature sensor: a Type K Temperature Sensor (i.e., a thermocouple). What is a thermocouple thermometer? How does it work? EXPERIMENT # 2 Measuring the Specific Heat of Metals Experimental apparatus to measure the specific heat of common metals – copper (Cu) & aluminum (Al). Some groups measure Cu and others Al. We’ll compare results at the end. Which do you think has higher specific heat? Predict: Cu___, Al____. Power Supply Thermocouple Interface Heater Thermocouple sensor Metal block (Cu, Al, …) Styrofoam thermal insulation A thermocouple sensor consists of a pair of wires of different metals welded together at one end. Because electrons in the two wires diffuse from the hot end to the cold end at different rates, a voltage is generated between the ends of the wires that is proportional to the temperature difference between the weld and room temperature. In a Type K thermocouple, the wires are made of chromel and alumel (two alloys). The sensor is calibrated to read out the temperature of the weld. V

©University of Illinois at Urbana-Champaign Physics 213 Lab 2 Summer 2023 Edition Page 7 of 14 Important Note: If you see strange temperature results, the protective, electrically insulating layer of nail polish on the end of the thermocouple probe may have been damaged or removed. If this is protective layer is not there, ask your TA to apply another coating of nail polish on the end of the probe. Predictions: In the graph provided below, sketch your prediction for how the temperature of the Cu (or Al) block will vary as a function of time after the heater is turned on (solid line). Below, explain your reasoning for the sketch you drew. ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ THEORY: The specific heat c of a material is the heat energy per unit mass required to raise the temperature of the material by 1 K: 1 dU c m dT  Temperature (C) Time (sec.)

©University of Illinois at Urbana-Champaign Physics 213 Lab 2 Summer 2023 Edition Page 8 of 14 If c is constant 1 , we can calculate 2 it from the total heat energy supplied Q (= P  t for constant power P supplied for a time duration  t) and temperature increase  T: 1 Q P t c m T m T      . 9. Test your predictions. Click the “Record” button to start the data acquisition. 10. After 20 seconds have elapsed, turn ON the power supply. Record the voltage and the current below (you will need them to calculate the average power). After 130 seconds, switch the power supply OFF. Continue taking data for 30 additional seconds and then click on STOP. Record the measured heater voltage, current and calculated power here; also enter the calculated power in the table in the Analysis section below: V = ______ Volts I = ______ Amps P = (V*I) = ______ Watts 1 In metals, in addition to the lattice vibrations, the electron “gas” also contributes to the specific heat, and the contribution depends on the temperature. However, at room temperatures, this is a small correction to the specific heat, so we neglect it here. 2 In general, c is a function of temperature; for constant power input, the specific heat at a given temperature, T, is related to the (local) slope, dT(t)/dt, of the T-vs.-t curve at time t: 1 / ( ) ( ) / dU dt P T t c T m t m dT dt                 .

©University of Illinois at Urbana-Champaign Physics 213 Lab 2 Summer 2023 Edition Page 10 of 14 Questions: How did your measurements of the Temperature T(t) versus time t compare with your predictions? ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ How did your calculated value of the specific heat compare with the book value? What are possible sources of errors in your calculated value? ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ EXPERIMENT # 3 Measuring the Thermal Conductivity of Metals In this experiment, we will measure the thermal conductivity of Cu and Al. Some groups measure Cu and others Al. We’ll compare results at the end. Predictions: The thermal conductivity of a material describes how well it can transport heat. Touch both the copper and the aluminum rod. Which “feels colder”? ______________________________________________________________ Which do you think has higher thermal conductivity? Predict: Cu___, Al____. Insulation Heat sink Thermocouple T A Thermocouple T B Heater Sample rod

©University of Illinois at Urbana-Champaign Physics 213 Lab 2 Summer 2023 Edition Page 11 of 14 1. Connect a second ‘ Type K temperature sensor ’ in PasPort 2. 2. Open the file: “ P213-Lab2_Experiment 3 - PasPort Sensors.cap ” . 3. Locate the 1.27 cm diameter Copper or Aluminum rod. There is a big hole in one end for the heater, and two small holes (separated by 10 cm) in the side of the rod for two thermocouple sensors. Insert the end (opposite the heater hole) into the large heat sink, using a small amount of thermal grease. Insert the heater into the hole at the top end of the rod, using a small amount of thermal grease. 4. Slide the three pieces of foam pipe insulation onto the copper rod such that the side holes can be seen through the gaps in sides of the foam pipe insulation. 5. Insert the thermocouple sensor from PasPort 1 into the upper hole in the side of the rod, and insert the thermocouple sensor from PasPort 2 into the lower hole in the side of the rod. Hold them in place by sandwiching them between adjacent sections of the foam pipe insulation. Predictions: In the graph provided below, sketch your predictions for the time dependence of a) the average temperature of your Cu (or Al) rod (solid curve) and b) the temperature difference between the upper and lower side holes (dashed curve). Assume that the heater is turned on at t = 0. Explain your reasoning for the sketch. ______________________________________________________________ ______________________________________________________________ ______________________________________________________________

©University of Illinois at Urbana-Champaign Physics 213 Lab 2 Summer 2023 Edition Page 13 of 14 THEORY: The thermal conductivity,  [Watts/m 2 -K] of a material is the heat current density, J (= heat energy per unit time per unit cross-sectional area, J = H/A where H = dQ/dt = heat current = power applied, P [Watts = Joules/sec] and A [m 2 ] is the cross-sectional area of the material) that flows through a material when a temperature gradient  T (= dT/dx ≈  T/  x, in one dimension) is applied: / / / J H A H A T T dT dx       . For a rod of uniform cross-sectional area A and length,  x = x 2 - x 1 = L,  can be found from the power applied and the temperature difference,  T = T A -T B : P x P L A T A T       . ANALYSIS: 1. Using the data in your table and graph of the T diff vs. time, determine the value that T diff asymptotically approaches. Use this value as the steady-state temperature difference  T in the table below. 2. Calculate the thermal conductivity  for the copper (or aluminum) rod using the above formula and record the values for  Cu (or  Al ) in the table below. Note that the relevant length for the copper and aluminum rods is the distance between thermocouples, L = 10 cm = 0.100 m. Note also that both copper and aluminum rod diameters are D = 1.3 cm = 0.013 m. 3. Write your measured value of  on the board to compare with others. 4. Delete all data runs. Close the file. DO NOT SAVE THE FILE!!! 5. Unplug the ‘Type K Temperature Sensor’ from PasPort 2 of the PASCO box.

©University of Illinois at Urbana-Champaign Physics 213 Lab 2 Summer 2023 Edition Page 14 of 14 Copper Aluminum Mass Density,  (kg/m 3 ) 8900 2700  T (K) Power, P (Watts)  (experiment) (W/m-K)  (book value) (W/m-K) 401 235 Questions: In words, how did your experimentally determined value of the thermal conductivity 3 of copper (or aluminum),  Cu (or  Al ) compare with the book value? ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ What are possible sources of errors? ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ FINISHING UP: When you have completed the lab, please carry out the following clean-up steps: 1. Empty all water containers and dry up any spills or drops. 2. Turn off the AC power strip that is used for the DC power supply on your table. 3. Organize all equipment, samples, and tools neatly on your table. 4. Turn in your lab write-up. Attach the graphs that you have plotted. In short, leave the lab as you found it -- or would have wanted to find it. 3 Note that, just as the specific heat is not constant for metals, the thermal conductivity also varies with temperature (above room temperature  typically decreases slightly with T). However, over a limited temperature range in the vicinity of room temperature (~20 o C),  is reasonably constant.