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When the temperature of an object changes from a given temperature T1 to a final temperature T2, a certain amount of heat Q is transferred either to or from this object. This amount of heat depends on the mass m of the object, on the temperature difference (T2 – T1) and on the specific heat c of the material the object is made of, and is given by: ( ) T2 T1 Q ? cm ? . (1) In this laboratory Q is measured in calories (cal), m in grams (g), T in degrees Celsius (?C) and c in cal/g?C. The specific heat of an object c is a positive quantity which provides a measure of the “ease” or “difficulty” with which the temperature of the material the object is made of, can be raised or lowered. For the purposes of this laboratory, the specific heat of all objects c is assumed to be independent of their temperature T. The measurement of heat quantities by the method of mixtures makes use of the First Law of Thermodynamics (conservation of energy), in the following sense: when heat transfer takes place between two bodies initially at different temperatures (Ti for the combination of tap water and the calorimeter cup, and Ts for the warmed-up metal cylinder), the quantity of heat lost by the warmer body (metal cylinder) is equal to the amount of heat gained by the cooler bodies (water and calorimeter cup). As a result, 52 the system of calorimeter cup with water and metal cylinder eventually reaches an intermediate temperature Tf. We have tacitly assumed that the system is isolated, so no heat is exchanged with its environment. In this experiment, the isolation is provided by the calorimeter. Let ms be the mass of the solid cylinder, mc be the mass of the calorimeter cup (without the gasket) and mw be the mass of tap water that we put in the calorimeter cup. The corresponding quantities for the specific heat are: cs for the solid cylinder, cc = 0.22 cal/g?C for the calorimeter cup (which is made of aluminum) and cw = 1 cal/g?C for water. Then ( ) ( )( ) s s s f c c w w Tf Ti c m T ?T ? m c ? m c ? . (2) Following equation (2), we find the specific heat of the material the solid cylinder is made of ( ) ( )( ) s s f c c w w f i s m T T m c m c T T c ? ? ? ? . (3) PROCEDURE: Measurements: 1. Check the level of water in the water boiler and add water if necessary. Plug in and turn on the water boiler. 2. Find out of which material (Sn: Tin, Zn: Zinc, Cu: Copper, Pb: Lead) is the metal cylinder that are you are using made. The chemical symbol of the material of each cylinder is stamped on it. Chemical element: _____________________ 3. Using the Triple Beam Balance, determine the mass ms of the metal cylinder: ms = _______________________________ g and the mass mc of the empty calorimeter cup: mc = _____________________________ g. 4. Fill almost half of the calorimeter cup with tap water and weigh it: mc + mw = _____________________ g. 53 5. Replace the calorimeter cup in its insulating jacket. Measure the temperature of the tap water in the calorimeter cup (in degrees Celsius): Ti = ______________________ ?C. 6. Suspend the metal cylinder above the surface of water in the boiler. Heat the water in the boiler until it boils. Allow the cylinder to be heated for a few minutes. The metal cylinder should not be touching the bottom or the sides of the boiler. 7. Measure the temperature Ts of the boiling water (or the same: The temperature of a hot metal cylinder): Ts = ______________________ ?C. 8. Transfer quickly the metal cylinder from the boiler to the calorimeter. Cover the calorimeter with its plastic lid. Gently stir the water in the calorimeter. After a few minutes, measure the equilibrium temperature Tf of this system (in degrees Celsius): Tf = ______________________ ?C. 9. Turn off and unplug the water boiler. Calculations: 10. From the previous measurements, calculate the mass of tap water: mw = (mc + mw) – mc = ________________________ g. 11. Substituting the above data in equation (3), calculate the measured value cs: cs = ____________________ cal/g?C 12. Read the accepted value of cs from Table II (page 87 of these Lab Manuals): cs accepted = ____________________ cal/g?C 13. Calculate the % Error of specific heat cs: ? ? ? % ? 100% s accepted s s accepted c c c Error ____________________ %. QUESTION: Which of the two following materials, water or aluminum, needs more heat per unit mass to have its temperature increased from 20 ?C to 30 ?C? Justify your answer. 54 Student Name __________________________ Section _______________ Date ___________ Report on Laboratory Experiment “Specific Heat of a Solid” DATA TABLE 1 Chemical element of which the metal cylinder is made 2 The mass of the metal cylinder ms g 3 The mass of the empty calorimeter cup mc g 4 The mass of the calorimeter cup with tap water mc + mw g 5 The mass of tap water mw mw = (mc + mw) – mc g 6 The temperature of the tap water in the calorimeter cup Ti ?C 7 The temperature of the boiling water Ts or the same: The temperature of a hot metal cylinder ?C 8 The equilibrium temperature of the system Tf ?C 9 The measured value of specific heat cs cal/g?C 10 The theoretical (accepted) value of specific heat cs accepted (from Table II, Appendix, page 73) cal/g?C 11 The % Error of specific heat cs %
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