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ABSTRACT Heat capacity is a form of energy which transfers among particles in a substance (or system) by means of kinetic energy of those particles. This paper discusses how to determine the specific heat of a metal and the latent heat of fusion of an ice. This experiment will prove the theory behind heat and calorimetry which is Q=mcDT.

INTRODUCTION Heat is the form of energy that may be transferred if there is a difference in the temperature. The amount of heat, Q, required to raise the temperature of a solid body at constant pressure depends on the change in temperature, DT, of the body, its mass, m, and a characteristic of the material forming the body called its specific heat, C. This relationship is expressed by the equation Q = mCDT and the dimensions of C are thus heat per unit mass per unit temperature change. The values of C do depend on temperature with those of common metals such as aluminum and brass increasing a few percent as the temperature increases from 20°C to 100°C, for example, while that for iron or steel increases about 10% over the same range. Since these are not large changes, average specific heats are often quoted in handbooks for such fairly broad temperature ranges. Historically the amount of heat, Q, was originally expressed in terms of calories. The calorie was defined most accurately as the amount of heat required to raise the temperature of 1 gram of water from 14.5°C to 15.5°C at 1 atmosphere pressure. With this definition the specific heat of water between 0°C and 100°C is 1.00 cal/gm×°C to within better than 1%. The use of the calorie began before it was established that heat was a form of energy and that 1 calorie is the equivalent of about 4.18 Joules. Thus in the SI system of units specific heats, that is the values of C for particular materials, are expressed as J/kg×°C and there is no need for the calorie. However, since so much work involving heat has used the calorie and since the specific heat of water is unity when it is employed, it remains a common unit and will be used in this work. The food Calorie, with a capital C is 1000 of these calories or 1 kilo-calorie.

The process of measuring quantities of heat exchanged is called calorimetry. In this experiment the objective is to determine the specific heat of a metal and to determine the latent heat of fusion of ice. Theory: We know that when two bodies, initially at different temperatures, are placed in intimate contact, in time they will come to equilibrium at some intermediate temperature. Provided no heat is lost to or gained from the surroundings, the quantity of heat lost by the hotter body is equal to that gained by the colder body. This is the process which occurs in the method of mixtures that you will use. The metal sample whose specific heat is to be measured is heated in boiling water to about 100°C. It is then quickly transferred to an aluminum calorimeter cup which contains cold water of known temperature. When the metal sample and calorimeter cup come to equilibrium, the common temperature is measured with a thermometer. It is assumed that the transfer of heat between the thermometer and the system is small enough to be neglected. If the net heat exchange with the surroundings can be kept small, then the heat lost by the metal sample equals the heat gained by the water and the calorimeter cup. Let Ms be the mass of the sample whose specific heat is Cs. Let Ts be its temperature before it is placed in the calorimeter. Let Mw and Cw be the mass and specific heat of the water and let Mc and Cc the mass and specific heat of the calorimeter cup. Denote the temperature of the water and calorimeter cup before the sample is added by Tw and the final temperature of the mixture by Tf. Now use these42 symbols to express mathematically the situation when a hot object (the sample) is placed in contact with a cooler one (the water and the calorimeter cup) and the two are allowed to exchange heat until they reach a common temperature. From this equation derive an expression for the specific heat of the sample in terms of the other quantities.

METHODOLOGY This experiment is entitled “heat and calorimetry” and is divided into two parts. First part is determining the specific heat of metals. The materials used are electric stove, calorimeter, thermometers, copper metal, aluminum metal, beaker, weights, digital weighing scale and a cup ice. In part 1 of the experiment we must boil water in the beaker and then immerse the metal in it, one metal at a time. In this part, it is important to immerse the metal in the boiling water for a long time because we need to heat up the metal to absorb heat from the boiling water, so that if we transfer the metal in the calorimeter, we can get a loss error result. In the other hand, if we immerse the metal for a short period of time, the metal will not absorb more heat that will heat up the calorimeter. Let the metal absorbs heat first and then measure its temperature using thermometer. We need to wipe off the excess water that remains in the metal, because it can affect the initial temperature. Water in the metal has different temperature than the metal that can have a result of error in the experiment. And once measured, put the heated metal in the calorimeter with tap water in it and then measure the calorimeter. Using the Law of Heat exchange, a derived equation was made to solve for the specific heat of the metal. We computed for the percent error by referring to table 1 for the actual specific heat of the aluminum metal.

In part 2 of the experiment, we are required to get the latent heat of fusion of ice. We measure the calorimeter, water and the temperature of water and ice. We put the ice in the calorimeter and melt it. Our initial temperature of ice is 0ºC. Since, it is hard to determine the initial temperature of ice; we assume the initial temperature of ice by means of its property that ices have a freezing point of 0ºC and melting point of 0ºC. We get the value of mass of ice by subtracting the total mass from the water and calorimeter. And once the ice is being moved into the calorimeter, it is important to wipe off the water from the surface of the ice, because excess water can affect the mass of the ice when measuring it after melting it in the calorimeter. Since we don't need the excess water, we could rather wipe it off to get less error. If there will be a different mass of ice, then the latent heat will depend on the mass of the ice. We determine the percentage error using 80 cal/g as the actual value of latent heat of ice.

ANALYSIS This table is the Specific Heats of Substances and in this table is where we will be comparing the results of what we get in the experiment. In the first part of the experiment, after doing the step by step procedures, we got 48 temperature for aluminum and 59 also got 22

and 22

initial

for copper metal. We

respectively for the initial

temperature of calorimeter and an initial temperature of 25

for water in aluminum and copper

metal. The final temperature of mixture for aluminum is 29

while for copper is 16 . The

experimental specific heat of aluminum metal is 0.2406 cal/gcopper metal, the experimental specific heat is 0.0936 cal/g-

having a %error of 1.20%. For having a 2.07% error.

It is important to immerse the metal in the boiling water for a long time for it to let the metal gain some heat so that it will reach its thermal equilibrium with the boiling water. The water needs to be wipe off from the metal surface before dropping it into the calorimeter because the water will have an additional temperature when it’s place on the calorimeter. The mixture will have inappropriate equilibrium temperature. One advantage of using the stirrer of the calorimeter in mixing the metal and water because it will shorten the time to reach the thermal equilibrium of the mixture. In the second part , the experimental latent heat of fusion of ice is 79.0676 cal/g while the actual value is 80 cal/g. this have a percentage error of 1.655%. this means that there is only a minimal error in the experiment. For this part, the initial temperature of ice is 0 . In this part, it is also important to wipe off the water from the ice’s surface before putting it in the calorimeter because excess water can affect the mass of the ice when measuring it after melting in the calorimeter.

CONCLUSION Our group was able to determine both the specific heat of the two metals given, Aluminum and Copper. Another thing is to determine also the fusion of ice.

The experiment shows how heat of the surrounding can affect the temperature of an object. Heat can be defined as the form of energy transferred to another object. There must be a difference in temperatures of the substance to have heat or energy transfer. The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius. The relationship between heat and temperature change is expressed in the form shown below where c is the specific heat. The relationship does not apply if a phase change is encountered, because the heat added or removed during a phase change does not change the temperature. By this formula, we can see the relationship of heat to mass and temperature. Heat is directly proportional to mass and change in temperature. The object needs more heat, which means greater final temperature, if there is greater mass, and vice versa. Also, from the equation and after the experiment, I can conclude that heat absorb by the metal depends on the property of the metal to absorb heat. The more heat it absorb the lesser the specific heat of that metal. They are inversely proportional to each other. Another thing is mass of ice is inversely proportional to the latent heat. The more weight the ice contain, the lesser the latent heat of fusion.

In the first part, the possible sources of errors are the time the metal is immersed in boiling water, the measurement of temperature and the room temperature, since we are performing in the laboratory with air conditioned room. This can be minimized by performing the experiment fast and consistent. In the second part, the possible sources of errors are the room temperature, The mass of ice before and after putting it in the calorimeter and the measurement of temperature.

REFERENCES http://www.physics.fsu.edu/users/ng/courses/phy2048c/lab/calorimetry/calorimetry.pdf http://www.chm.davidson.edu/vce/calorimetry/heatcapacity.html