# Specific Heats of Metals

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1 Johnson 1 Cameron Johnson Jun Li Physics 222 March 6, 2013 Specific Heats of Metals Abstract The purpose of this lab is to determine the specific heat of various types of metals by adding a known amount of heat to a known mass of metal, measuring the temperature change, and applying given formulas to our results. Introduction Specific heat is defined as the amount of heat necessary to raise the temperature of a unit mass of a substance by one unit temperature interval. Different materials have different specific heats based on their internal structure at the microscopic level. This means that different substances require different amounts of heat to raise their temperature a certain amount. Water, for example has a specific heat of 1 cal /-g C meaning that it takes 1 calorie (4.186 J) of heat to raise the temperature of one gram of water by 1 C. We can determine the specific heats of various materials by adding a known amount of heat to a sample of known mass of the material, measuring the temperature change, and inputting this data into given equations that relate specific heat to change in heat and change in temperature. We can achieve this by heating a substance of known mass to a known temperature and then mixing it into another substance of known mass and known colder temperature. This mixing will cause the hot substance to lose heat, and the cold substance to gain heat until the two substances reach the same temperature and are in equilibrium. If the mixing takes place in an enclosed in an insulated

2 Johnson 2 container so that no heat is lost or gained from outside sources, the law of conservation of energy tells us that the lost heat must equal the gained heat. This type of procedure is called the method of mixtures, and if we input the results into given formulas, we can determine the specific heats o each substance. Theory Definitions & Formulas: Specific Heat (c): amount of heat necessary to raise the temperature of 1g of a substance 1C. Heat Capacity (C): the constant of proportionality for specific heats. Temperature (T): the property that determines whether an object is in thermal equilibrium with other objects. Heat (Q): the transfer of energy across the boundary of a system. calorie (cal): a unit of heat defined as the amount of heat required to raise the temperature of 1g of water 1C. Mass (m) Method of Mixtures: a way of determining the specific heat of a material experimentally by measuring the temperature change of a given mass of material produced by a quantity of heat. This is done by bringing together several substances at various temperatures which will result in the hotter substances losing heat and the colder substances gaining heat until all the substances reach a common equilibrium temperature. If the system is insulated so that no heat is lost to or gained from the surroundings, then, by the conservation of energy, the heat lost is equal to the heat gained. T is proportional to amount Q added (or removed) from it: Q T Q = C T Specific Heat: c = Q m Q = mm T c = Q m T c water = Q = 1 cal = 1 cal m T 1g 1C g C Heat Lost = Heat Gained: Q mmmmm = Q wwwww + Q ccc aaa sssssss m m c m T m T f = m w c w T f T w + m cc c cc T f T w = (m w c w + m cc c cc )(T f T w )

3 Johnson 3 Example of Heats of Calorimeter Setup: How to Use a Calorimeter. N.d. MiniScience.comWeb. 12 Mar < Experiment To begin this lab, a calorimeter, a stirrer, a boiler cup, an electric hot plate, two digital thermometers, a sample of steel slugs, a sample of aluminum slugs, a balance, and ice. We started the first trial by measuring out a sample of aluminum and then placing it in the boiler cup. We placed the boiler cup on the hot plate and began heating it. We submerged one of the thermometers into the aluminum and monitored the temperature until it reached a steady temperature. While the heat pad was heating the aluminum, we weighed the mass of the calorimeter, filled it about ¾ full with below room temperature water, and then weighed the mass of both. We recorded the results in our data

4 Johnson 4 tables. We then measured the initial temperature of the water with the other thermometer and recorded its value in our data tables. When the aluminum reached a constant temperature, we recorded the final temperature in our data tables. We then took the hot sample of aluminum and poured it into the water in the calorimeter. We submerged the thermometer into the mixture and then stirred it with the stirrer. We monitored the thermometer until the mixture reached a steady temperature which indicated that the water and metal were at an equilibrium temperature. We then recorded this final temperature in our data tables. For the second trial, we repeated the process from the first trial except this time we used a sample of steel instead of aluminum. We recorded all of our measurements in our data tables and then applied the equations given for this experiment. We then compared these results to the given theoretical values. Data/Calculations (Refer to attached tables)

5 Johnson 5 Questions pp Questions #1, 5 1. Distinguish between heat capacity and specific heat. Heat capacity C is the amount of energy needed to raise the temperature of a sample by 1 ; however, the specific heat c of a substance is the heat capacity per unit mass. 5. What is the method of mixtures, and how is it used to determine specific heat? The method of mixtures is a method that mixes several substances at various temperatures together, the hotter substances lose heat and the colder substances gain heat until all the substances reach a equilibrium temperature. When a known amount of the hot solid is combined with a known amount of the liquid in a calorimeter, and the changing temperature are measured, we can use equation C m = (m wc w +m cs c cs )(T f T w ) to calculate the specific heat of that solid. m m (T m T f ) pp Questions #1, 3, 4 1. (a) The percent errors of your experimental values of the specific heats may be quite large. Identify several sources of experimental error. Sources of error could include possible splashing of water resulting in lower cold water mass and a higher equilibrium temperature, and possibly the temperature not being completely steady when we measured it at each stage of the experiment. (b) Why does it improve the accuracy of the experiment if T f T r T r T w? The larger the difference in temperature a substance is from the temperature of its surroundings, the faster it will increase or decrease in temperature toward the surroundings temperature. Because both

6 Johnson 6 the hot metal and cold water are exposed to the room temperature for a short amount of time before they are mixed, they will both change in temperature toward the temperature of the room slightly. If the initial temperatures of both the metal and the water are the same difference from room temperature, the metal will cool and the water will heat at the same rate making the result more accurate. If the differences are not the same, each substance will change in temperature at a different rate and the end result will be less accurate. 3. (a) If wet shot had been poured into the calorimeter cup, how would the experimental value of the specific heat have been affected? If the wet shot had been poured into the calorimeter cup, the final temperature reading would be lower than that of with the dry shot because it brought more cold substances. From equation C m = (m w c w +m cs c cs )(T f T w ) m m (T m T f ), the experimental value of the specific heat would be lower than it should be. (b) If some water had splashed out as you were pouring dry shot into the cup, how would the experimental value of the specific heat have been affected? If some water had splashed out, the final temperature would be higher than that of which the water had not splashed out because it lost some cold substances; therefore, from equation C m = (m wc w +m cs c cs )(T f T w ), the experimental value of the specific heat would be higher than it should m m (T m T f ) be. 4. In solar heating applications, heat energy is stored in some medium until it is needed (e.g., to heat a home at night). Should this medium have a high or a low specific heat? Suggest a substance that would be appropriate for use as a heat-storage medium, and explain its advantages.

7 Johnson 7 It should have a lower specific heat and the substance should be lead because it has a very low specific heat and is relatively inexpensive. Because of the lower specific heat, this type of material will have a lower changing energy thus will store the energy longer: c = Q m T Discussion In this experiment, we were able to determine the specific heats of aluminum and steel by inputting the masses of and temperatures of the samples and water of before mixing and the equilibrium temperature after into the given specific heat formulas. From our results, we found that the specific heat of aluminum was 883 J/kg C and the specific heat of steel was 440 J/kg C. When we compared these results to the accepted values of 900 J/kg C for aluminum and 448 J/kg C for steel, we found that our percent of error was relatively low. The error turned out to be -1.91% for aluminum and -1.68% for steel. Sources of error could include possible splashing of water resulting in lower cold water mass and a higher equilibrium temperature, and possibly the temperature not being completely steady when we measured it at each stage of the experiment.

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