79 5. Having carefully observed and recorded the temperature Tw of the wa- ter, quickly place the hot mass into the calorimeter. Stir the water, being careful not to spill any. After the metal mass and water come to equi- librium, measure and record the equilibrium temperature, Te. 6. Repeat steps 4 and 5 for the two remaining metals. Analysis of Data 1. Calculate the specific heat cx of each metal using Eq. 12.3. To simplify your calculations in determining the uncertainty in cx, use the high-low method and assume that the uncertainties in the masses and in the spe- cific heats of water and the calorimeter are essentially zero. 2. Calculate the % difference between each of your experimental values of cx and the value listed for that metal in Table 12.2. Does the value listed in the table fall within the uncertainty limits? Comment in the Conclu- sion section. Summary of Results Complete the Summary of Results table on the Analysis page spreadsheet. of your Conclusion Don't forget to include a table summarizing your final results. When discussing agreement between experimental and expected val- ues, be sure to explicitly discuss the overlap of the range of values indicated by their uncertainties. Percentage difference does not necessarily indicate agreement between two numbers. 1. Comment upon the results of the three specific heats measured in this lab. Are they acceptable in view of the uncertainty limits? 2. If the agreement is not acceptable, could unmeasurable heat loss ac- count for the discrepancies? To answer, you must first determine wheth- er unmeasurable heat loss would result in too large or too small a value of the specific heat. Explain. daldwin 3. You probably noticed that the percentage uncertainties in your specific heat values are large. What experimental factor is chiefly responsible for this? 75 #12 Specific Heat of a Metal Objective The objective of this experiment is to learn what specific heat is and how it differs for various metals. Introduction and Theory Thermodynamics is the field of physics concerned with the relations between heat (a form of energy) and mechanical energy or work, and the conversion of one into the other. The macroscopic quantities associated with this branch of physics include pressure, volume, temperature, internal energy and entropy among others. In this experiment we will deal with the flow of energy from one system to another. The flow of energy from a hot- ter body to a colder body is called heat. The terms heat and temperature have quite different meanings. Heat is the energy transferred between two systems as a result of a temperature difference. The temperature determines the direction and rate of heat transfer between systems. Temperature is a property of matter and heat is energy that is flowing because of a temperature difference. When heat en- ters a system, the internal energy of the system is increased. The transfer of heat, however, is not the only method of changing the energy of a sys- tem. When work is done on a system, its energy is also increased. Heat and work therefore constitute two different methods of adding energy to or ex- tracting energy from a system. After the transfer of energy has occurred, it is impossible to say whether the energy that now resides within the system is the result of heat or work. All one can do is to refer to the “energy” of the system. It is clear, therefore, that no meaning can be attached to the unfortunate expressions “the heat in a body” or the "work in a body.” It is impossible to separate the energy inside a body into two parts, one due to heat and one due to work. Although heat is a form of energy and hence could be measured in or- dinary units of work, it has been found desirable to establish arbitrary units of heat which are based upon the effect of heat in changing the tem- perature of the universal substance, water. In the metric system, the calo- rie is defined as the heat required to raise the temperature of one gram of water by one degree Celsius (more precisely, from 14.50 to 15.5°C). Substances differ in the amount of heat needed to produce a given rise of temperature in a given mass. For example, suppose that an insulated beaker contains 100 g of water at 45°C and that we wish to raise the tem- perature of the water to 50°C by adding different amounts of water or oth- er substances which have been heated to 100°C. Table 12.1 shows how much of four different substances would be required in order to bring about the desired temperature increase. 76 Substance at 100°C Mass (g) Mass (g) Substance at 100°C Copper 10 Water 108 Aluminum 46 Lead 328 Table 12.1. The amounts of four different substances at 100°C required to raise the temperature of 100 g of water at 45°C to 50°C. As can be seen from Table 12.1, one would need only 10 g of water, but 46 g of aluminum, 108 g of copper, and 328 g of lead, each at 100°C, in order to raise the temperature of the water in the beaker from 45°C to 50°C. Since substances vary in the amount of heat that is needed to pro- duce a given temperature rise in a given mass, we define a quantity called the heat capacity, C, given by the ratio of the heat Q supplied to a body to produce a temperature rise AT. Q (12.1) AT Since the amount of heat needed is dependent on the mass m of the body, we define a quantity, c, called the specific heat, as heat capacity (12.2) mΔΤ C = Q c= mass As may be seen from Eq. 12.2, the specific heat is numerically equal to the amount of heat required to change the temperature of a unit mass of the substance one degree. Hence, c is numerically the heat in calories re- quired to raise the temperature of 1 gram of a substance by 1°C. Table 12.2 lists some of the specific heats of common substances. Note the high specific heat of water. In the determination of thermal constants, the method that is most commonly used is known as the “method of mixtures.” This method is based upon the fact that if two or more bodies, originally at different tem- peratures, are placed in thermal contact and the transfer of heat takes place exclusively between these bodies, the energy given up by one part of the system is equal to that gained by the other. One of the simplest experi- mental determinations of the specific heat by the method of mixtures is to immerse in water a metallic object of known mass and initial temperature but unknown specific heat. By measuring the resulting equilibrium temper- ature of the water and metal, the heat absorbed by the water and the con- taining vessel can be easily computed and equated to the heat given up by the unknown metal. From this equation the unknown specific heat can be computed. 77 Substance Air (const, volume) Air (const. pressure) Alcohol Aluminum Brass Copper Ether Glass (crown) Glass (flint) Gold c (cal/g-°C) 0.168 0.237 0.65 0.22 0.090 0.093 0.56 0.16 0.12 0.031 0.5 Substance Iron Lead Mercury Nickel Platinum Steel Tin Turpentine Water Zinc e (cal/g-°C) 0.11 0.031 0.033 0.109 0.0323 0.118 0.055 0.46 1.000 0.092 Ice, 0°C Table 12.2. Table of specific heats (in cal/gº-C) for different substances. The basic device for measuring the quantity of heat absorbed or given off by a system undergoing a temperature change is a calorimeter. For dif- ferent thermal measurements, various types of calorimeters are used. One of the most common and simplest of these consists of a thin polished ves- sel of high thermal conductivity held centrally within an outer jacket by means of a non-conducting support. Thus, conduction of heat is mini- mized, while the “dead” air space between the inner and outer vessels helps to prevent heat transfer by convection currents. Radiation of heat is reduced by having the vessels highly polished. A wooden cover minimizes convection currents above the calorimeter cup. If the mass mx of the “unknown” specimen at a temperature Tx is placed in a calorimeter of mass mc and known specific heat ce containing mw grams of water at a temperature Tw, the temperature of the specimen will fall and that of the calorimeter and water will rise, so that the result- ing mixture will finally come to some intermediate equilibrium tempera- ture Te. The absolute value of the change in temperature of the specimen is thus (Tx - Te) and that of the water and calorimeter (Te - Tw). If no heat has been gained from or lost to the surrounding objects, it follows that Heat given off by specimen = Heat gained by water + heat gained by calorimeter. Substituting the above symbolic values for these quantities yields cxmx(Tx - Te) = Cwmw(Te - Tw) + ccm(Te - Tw) (12.3) Solving for cx gives a working equation in which all the quantities have been experimentally determined. As previously stated, the working equation, as derived, holds true on- ly as long as there is no heat transfer to or from the room. This condition is approximated by the use of a properly constructed calorimeter and by having the water at an initial temperature about as much below room tem- perature (say 2') as the resulting mixture will be above room temperature. 78 In this way, the error due to the little heat that is absorbed from the room (while the temperature of the water is below room temperature) will be compensated for by the error due to heat lost to the room (while the tem- perature of the mixture is above room temperature), or vice versa. With reasonable care, the specific heats of substances can be determined by the method of mixtures with an error not exceeding 1%. Comparisons of ex- perimental values with those found in tables are often misleading because of the wide variations in the purity of the materials used. Apparatus Check that you have the following items on your lab table: pan balance electric hot plate thermometer with Celsius scale calorimeter cup, stirrer, and insulating outer vessel samples of three different metals (attached to strings) glass flask (boiler) extra cup to carry water from sink heat protective gloves - - - - - Experimental Procedure Note: Uncertainties should be estimated and recorded for each measured quantity in all experiments! 1. Fill the boiler about one-third full of water and start heating it with the cover off. 2. Weigh the (empty) inner vessel of the calorimeter (without the fiber ring but with the stirrer). Record the material of the calorimeter. 3. Write down the name of each metal for which you will determine the specific heat. Determine each metal's mass, and place it in the boiler. When it comes to thermal equilibrium wih the boiling water, its temper- ature will be 100°C. In the transfer, the metal will cool somewhat. We will assume a temperature of Tx = (95 + 5)°C for the metal when put in the calorimeter. 4. Add enough water at about 2°C below room temperature to cover the mass when it is placed in the cup. Weigh the calorimeter cup with the water. 0
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