Purpose

1. Purpose • Understand how the total energy in a closed system is conserved during heat exchange. • Learn how to determine specific heat capacities of certain materials.

2. The Heat Capacity of an Object Amount of heat (energy) that needs to be added to the object in order to raise its temperature by 1 degree Kelvin. Heat added (in Joules) Change in Temperature (in Kelvin) Heat capacity (in Joules/Kelvin) If Q > 0 then Tfinal > Tinitial (temperature rises) If Q < 0 then Tfinal < Tinitial (temperature drops)

3. The heat capacity depends on: • Type of Material • Amount of the material (more water has more heat capacity……… you need more energy to raise its temperature……… The specific heat capacity is defined as and has units of or The specific heat capacity only depends on the material, not on the amount of the material.

4. The Specific Heat Capacity Amount of heat (energy) per unit mass that needs to be added to a material in order to raise its temperature by 1 degree Kelvin. Heat added (in Joules) Change in Temperature (in Kelvin) Specific Heat capacity mass of the object

5. Example and Implications of Specific Heat Capacity A calorie is defined as the amount of heat that needs to be added to 1 gram of water in order to raise its temperature by 1 degree Kelvin. • Water has a relatively high heat capacity, which is important in biology and engineering: • Prevents your body (= mostly water) from heating up too quickly during exercise (an apple • that contains 60Kcal of energy has the potential to raise the temperature of a 60Kg • person by only • DT = Q/(c*m) = 60000cal/(1 cal g-1K –1 * 60000g)=1Kelvin • (assuming all the energy in the apple would go to heat and none to work performed) • Is a good coolant for engines (can absorb a lot of heat without having its temperature rise a lot.

6. m1 c1 m2 c2 m2 c2 T2, initial T2, final T1, initial Heat Transfer Between Two Objects(assume no heat is lost to the environment) Before contact: After reaching thermal equilibrium they both have the same temperature m1 c1 T1, final T1, final = T2, final = Tfinal Given: m1, m2, c1, c2, T1,initial, T2,initial (Tfinal unkown)

7. Because no heat is lost to (or gained from) the environment: The originally colder object gains energy (a positive Q) The originally hotter object looses energy (a negative Q)  Solve for Tfinal

8. Activity 1: Calibration of Temperature Probe Themocouples are very easily built temperature sensors. Two dissimilar conductors touching each other produce a voltage V that changes with temperature T. Over certain temperature ranges T is proportional to V and one can calibrate them by finding the voltage for two temperature points and then making a linear approximation. Thermocouple voltages can then be related to temperature. V Vhot Two calibration points Vcold T Thot Tcold

9. Activity 1: Calibration of Temperature Probe Alcohol thermometer (read off temperature here) Temp. Probe 750 Interface Use ice bath and warm water bath for the two calibration points

10. Activity 2: Determining thePower Output of the Heater Styrofoam cup filled with 150 ml water. Make sure heater doesn’t touch styrofoam !!!!! Stand + clamp Red LED: Heater is ON Computer: Capstone Switches Heater on/off heater Heater Switch Box Temp. Probe 750 Interface Make sure this is plugged in the right way (ground to ground); ground is marked on tape

11. Activity 2: Determining the Power Output of the Heater Observe total temperature change DT due to heating: First part with heater on Temperature DT After switching heater off. time Turn Heater off (Turn off “Signal Generator” in Capstone) Heater on Dt

12. Activity 2: Determining the Power Output of the Heater Click here to open signal generator panel • First click on “Auto” : This ensures that when you hit “Record” the heater automatically starts with the recording. • Click on “Record” (lower left corner of Capstone). • After a fixed (known) amount of time stop just the heater (but not temperature measurement) by clicking “OFF”. • To stop temperature recording, click on the “Stop” button in the lower right corner.

13. Activity 2: Determining the Power Output of the Heater Power = Energy / time = c m DT / Dt This is the heat/energy given off to the water ( = “Q” ) Compare your result to the power rating written on the heating element.

14. Activity 3: Determine Specific Heat Capacity of Isopropyl Alcohol Design an experiment to measure c isopropyl alcohol • DO NOT DRAIN THE ISOPROPYL ALCOHOL INTO THE SINK !!!!! It is illegal to do that and we also do not want to waste the alcohol – it costs money. • Instead, please pour it back into the container from which you got it. Use your measured power rating of the heating element. Caution: Isopropyl alcohol is a flammable liquid. If you accidentally spill it over a power outlet, do not unplug the equipment. Sparks may ignite the alcohol!

15. Activity 4: The Transfer of Heat Caution: This experiment uses liquid nitrogen, which is extremely cold. Follow the safety instructions! Step 2: Put cold brass (-197ºC) into water. Step 1: Cool brass in the LN2 (wait until bubbling stops) Step 3: Monitor temperature Brass disc on a string Water at Room Temperature Liquid nitrogen (LN2)

16. Activity 4: The Transfer of Heat Step 4: Determine the specific heat capacity of brass Step 5: Compare your value of cbrass to that in the literature (you can surely find that value on the internet)

17. Hints • Do not be surprised if the power rating of the heater element disagrees with what you measured. When we measured the resistance of the heating elements with wires, some were as high as 2 Ohms. • Therefore, a more realistic power rating may be about • …and it may be even lower if the supplied voltage is less than 12 Volts (on some of the heater boxes)  That’s why you need to use your measured power rating in Activity 3, not the official rating.

18. Liquid Nitrogen Safety • Wear goggles when using liquid nitrogen. • Pour liquid nitrogen slowly and very carefully. • Do not deliberately spill liquid nitrogen. • When putting the brass object into liquid nitrogen, suspend it on a string and carefully lower it into the liquid nitrogen(the nitrogen will boil rapidly). • Do not touch liquid nitrogen or metal surfaces that are in direct contact with liquid nitrogen. • Never put liquid nitrogen into a closed container (except into specially designed containers with pressure relief and safety valves). It will explode and you may be seriously injured or killed by the exploding fragments. • When carrying liquid nitrogen to your table, walk carefully and make sure nobody bumps into you (or you into them). • When done with your liquid nitrogen, you can carefully pour it back into the dewar.