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Bellevue College PHY115 Physics Lab: SPECIFIC HEAT OF A METAL/HEAT OF FUSION OF WATER Purpose To review the relationships associated to flow of heat from a hotter (metal) to cooler object (water at room temperature). To understand and apply the principle of conservation of thermal energy – Heat energy gained by cold water is equal to heat lost by the hot metal. To determine the specific heat capacity of two unknown samples of metal in the temperature range between room temperature (water) and water boiling temperature (metal). To compare the accepted values of specific heat for 2 different metals Theory Heating is a result of energy transfer from object with higher temperature to an object with lower temperature. Two objects in contact that start at different temperatures will reach the same temperature – thermal equilibrium. If the two objects are enclosed in the environment that no heat is exchanged with surrounding, the amount of heat which flows from the hot object must equal the amount of heat which enters the cold object – the low of conservation of energy. As a result the thermal energy (heat) of the hotter object will decrease and that of the cooler object will increase. The metric unit for heat energy is Joule (J). Besides Joule, the unit of calorie “cal” is also used in metric system. A calorie is the amount of energy or heat, required to increase the temperature of one gram of water for one degree Celsius. The relationship between these two units is: 1 cal = 4.19 J or 1 J = 0.239 cal The amount of heat energy that is required to raise the temperature of one gram of a substance by one degree Celsius is called the specific heat capacity, or simply the specific heat of that substance. J or Joules per kilogram · Kelvin kg × K Water, for instance, has a specific heat of: 4190 Some examples of specific heats in Al: 900 Lead: 128 Cu: Iron: J kg × K J are: kg × K 385 449 Other specific heats are listed on p. 381 The amount of heat energy involved in changing the temperature of a sample of a particular substance depends on three parameters the specific heat of the substance (cv), the mass of the sample (m), Page 1 Last Updated:6/26/2017 Bellevue College and the magnitude of the temperature change. The Greek letter delta ( ) is used to indicate a change. T = temperature final - temperature initial The amount of heat energy that is transferred in the process of producing a temperature change can be calculated from this information, according to the following equation: Change in heat energy mass X specific heat X change in temperatur e Q m cv T In this experiment, you will determine the specific heat of a metal. A heated sample of this metal will be poured into cool water contained in a plastic foam cup. Shortly after mixing, the water and the metal will have come to the same temperature. Because plastic foam is a good insulator, heat cannot easily escape to the surroundings. Therefore, the heat lost by the metal can be said, for the purpose of this experiment, to be equal to the heat gained by the water. The amount of heat energy gained by the water will be calculated in the following formula: Heat gained by water mass of weater X specific heat of water X change in temperatur e of water Qwater mwater c water Twater The amount of heat energy lost by the metal will be calculated in the following formula: Heat lost by the metal mass of the metal X specific heat of the metal X change in temperatur e of the metal Qmetal mmetal cmetal Tmetal Because the heat gained must equal the heat lost, a third equation can be written. Qmetal Qwater mmetal cmetal Tmetal mwater c water Twater The specific heat of water is known. The temperature changes of the water, and of the metal, can be measured, as can the mass of the water and the mass of the metal. Using this data, the specific heat of the metal can be calculated using equation: cmetal mwater c water Twater mmetal Tmetal Page 2 Last Updated:6/26/2017 Bellevue College PROCEDURE: 1. Fill a 250-mL beaker about 3/4 full of water. Place the beaker on electric plate (see drawing). Use a electric plate to bring the water to a slow boil. While the water is heating, proceed to step 2. . 2. Obtain a sample of the metal being used that will fill the test tube about 1/4 full. Find the mass of the metal to the nearest 0.01 g and record on the table. 3. Transfer the metal into the inner container of the calorimeter. Place the metal on the “ring”. Position the test tube so that the metal is below the level of water in the beaker (be sure the bottom of the test tube does not touch the bottom of the beaker). Adjust the knob on the electric plate so the water is just boiling gently. Allow the test tube to remain in the boiling water bath for at least 10 minutes. Proceed to step 4 while the metal is heating. 4. Carefully measure out 100 mL water in a graduated cylinder, and pour the water into a plastic foam cup. Place the cup in a 400-mL beaker for support. Place a thermometer and stirring rod in the cup. Record on the table the mass of the 100.0 mL water sample. REMEMBER that 1 milliliter of water has a mass of 1 gram. 5. After the metal has been heating for at least 10 minutes, using the thermometer, measure the temperature of the hot water. The temperature of the metal is the same as the water. Record this temperature to the nearest 0.5 oC as the initial temperature of the metal sample in the table. Read the temperature of the water in the calorimeter to the nearest 0.5 oC and record in the table as the initial temperature of the water. 6. Remove the metal from the boiling water, using the clamp as a holder. Carefully, but quickly, place the metal into the water in the second cup (use a paper towel to keep any hot water on the tube from dropping). Note the temperature frequently. As the temperature begins to change more slowly, watch the thermometer continuously so as not to miss the maximum temperature reached. Record this maximum temperature on the table to the nearest 0.5 oC, as the final temperature of water and metal. Page 3 Last Updated:6/26/2017 Bellevue College DATA TABLE: Mass of Mass of the metal water in sample Metal calorimeter mmetal Sample mwater kg Initial temperature Initial Final of metal temperature temperature sample of water in of water and calorimeter metal kg K K K 1 2 3 4 CALCULATIONS TABLE: Change in Change in temperature temperature Heat energy Metal of water of the metal gained by specific heat Sample Twater Tmetal the water of the metal K J K J kg × K Error % 1 2 3 4 7. Calculate the changes in temperature of the water ( Twater) and of the metal shot ( Tmetal). These are just simple subtractions. Remember, the water and metal had the same final temperature, but different initial temperatures. Record the date on table. T = temperature final - temperature initial 8. Calculate the heat energy gained by the water. Use formula for Qwater from the introduction for this calculation. 9. Remember that the heat gained by the water is equal to the heat lost by the metal, calculate the specific heat of the metal using the formula for cv: . cmetal mwater c water Twater mmetal Tmetal The specific heat of water is again, in J kg × K Look up the specific heat for your metal on a textbook, and compare your experimental answer the questions. 10. Compare calculated values for the specific heats to those from textbook for the corresponding metal by calculating the % error values. Repeat the whole procedure for the second and third different metal sample. Page 4 Last Updated:6/26/2017 Bellevue College Questions and applications 1. If you double the mass of metal, keeping everything else the same, what will happen to the ΔT of the water in a beaker? 2. If you double the mass of water, keeping everything else the same, what will happen to the ΔT of the water in a beaker? 3. Calculate the amount of heat required to raise the temperature of 78.2g of water from 10C to 35C. 4. What is the specific heat of a 75 gram sample that requires 1200 cal to change the temperature from 25C to 85F? 5. Calculate the amount of heat, in joules, need to raise 34g of ice from 55C to 67C. 6. Calculate the specific heat for a 102g sample that requires 1430J to raise the temperature from 8.7C to 12.5C. 7. What will the final temperature be if, at room temperature (25C), 1300 cal are added to a 76g sample of iron? 8. What would the change in temperature (T) be if an 89g sample of copper required 678 calories of heat? 9. Convert the specific heat capacity values to units of J J Note: The units are the kg × K kg × K same as J/kg. oC, since a temperature change in oC is the same as a temperature change in K units 10. Calculate the % difference of the experimental values from the accepted values. Part II Heat of Fusion of Water Devise an experiment that will experimentally obtain the Heat of Fusion of Water (Solid/Liquid phase change). Be sure to include appropriate data tables, graphs, calculations and data analysis. Page 5 Last Updated:6/26/2017