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.

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)

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.

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

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.

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

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

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

Activity 2: Specific Heat Capacity / Power Output of Heater Styrofoam cup filled with 150 ml water. Make sure heater doesn’t touch styrofoam !!!!! Stand + clamp Red LED: Heater is ON Computer: Data Studio 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

Activity 2: Specific Heat Capacity Switch heater on and monitor the rise of the temperature First run with heater power connected. Temperature DT Second run with heater power disconnected from outlet. time Heater off Heater on Dt Note: The temperature may still rise after you turn the heater off (it gets turned off when you hit the “STOP” button in Data Studio). Problem: Data Studio stops monitoring the temperature after “STOP” is hit. Solution: After you hit the “STOP” button, unplug the main power (outlet) from the heater box. Then hit “START” again to monitor the temperature without further heating.

Activity 2: Specific Heat Capacity Determine power output of the heating element. 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.

Activity 3: Measure Specific Heat Capacity of Isopropyl Alcohol Design an experiment to measure c isopropyl alcohol Use your measured power rating of the heating element. 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.

Activity 4: The Transfer of Heat Caution: This experiment uses liquid nitrogen, which is extremely cold. Follow the safety instructions in your lab manual!!!! 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)

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)

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.