Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature Activity Overview Activity 1: Use relationship between transferred heat and temperature change to determine the maximum power output of a steam generator. Activity 2: Determine the specific heat of brass by dropping very cold brass into room temperature water and finding the equilibrium temperature.

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature 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) Heat capacity (in Joules/Kelvin) Change in Temperature (in Kelvin) If Q > 0 then T final > T initial (temperature rises) If Q < 0 then T final < T initial (temperature drops)

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature 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.

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature 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) Specific Heat capacity Change in Temperature (in Kelvin) mass of the object

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature 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  T = Q/(c*m) = 60000cal/(1 cal g -1 K –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.

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature Heat Transfer Between Two Objects (assume no heat is lost to the environment) m 1 c 1 T 1, initial T 2, initial m 2 c 2 Before contact: After reaching thermal equilibrium they both have the same temperature m 1 c 1 T 1, final T 2, final m 2 c 2 T 1, final = T 2, final = T final Given: m 1, m 2, c 1, c 2, T 1,initial, T 2,initial (T final unkown)

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature 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 T final

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature Activity 1: Measuring the Power Output of a Steam Generator Easy (in theory): 1) Take a measured amount of water (c known, m known) 2) Run the heater for an exact amount of time (time known). 3) Measure  T. 4) Calculate Power. If only it were so easy…….because it isn’t…… Water (warms up) Generated Heat

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature Activity 1: Measuring the Power Output of a Steam Generator Reality: 1)We won’t be able to heat just the water. Parts of the steam generator assembly will get hotter as well. 2)Our system isn’t perfectly insulated.  Some heat will be exchanged with the surrounding environment (net loss or gain). Container (warms up, too) Water (warms up) Heater Coil (warms up, too) Heat loss/gain to environment

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature Activity 1: Measuring the Power Output of a Steam Generator Container (warms up, too) Water (warms up) Heater Coil (warms up, too) Heat loss/gain to environment Assume: Neglecting heat losses/gains to environment: Minimize by having both gains and losses which (at least partially) cancel each other out (more on that later)

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature Activity 1: Measuring the Power Output of a Steam Generator If we take just 1 measurement (measure m,  T, time and know c for water) we have a mathematical problem: 1 equation, 2 unknowns (P and C o ) Solution: Repeat the measurement but change m or time. This will give you a second independent equation.  2 equations and 2 unknowns (solvable for both unknowns).

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature Activity 1: Measuring the Power Output of a Steam Generator

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature Activity 1: Measuring the Power Output of a Steam Generator Temperature probe 750 Interface Water (pre-cooled) Heater Coil Time in s Temperature versus time graph

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature Once you have determined P and C o……. Temperature probe 750 Interface Water (pre-cooled) Heater Coil Aluminum Mass 1) Measure the mass of the aluminum cylinder. 2) Predict the change in temperature for a given heating period. 3) Do the experiment and measure the actual change in temperature. 4) Compare theory versus experiment.

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature Activity 2: The Transfer of Heat Caution: This experiment uses liquid nitrogen, which is extremely cold. Follow the safety instructions in your lab manual!!!! Liquid nitrogen (LN2) Water at Room Temperature Brass disc on a string Step 1: Cool brass in the LN2 (wait until bubbling stops) Step 2: Put cold brass (-197ºC) into water. Step 3: Monitor temperature

Physics 1809 Minilab 2: Heat and Temperature The Relationship Between Heat and Temperature Activity 2: The Transfer of Heat Step 4: Determine the specific heat capacity of brass Step 5: Compare your value of c brass to that in the literature (you can surely find that value on the internet)