PHY12L - E302 - HEAT AND CALORIMETRY

ANALYSIS ON HEAT AND CALORIMETRY

          As an introduction, the definition of Heat energy (or just heat) is a form of energy which transfers among particles in a substance (or system) by means of kinetic energy of those particles. In other words, under kinetic theory, the heat is transferred by particles bouncing into each other. In physical equations, the amount of heat transferred is usually denoted with the symbol Q. Most of the times, heat may be mistaken as temperature.

In calorimetry it is often desirable to know the heat capacity of the calorimeter itself rather than the heat capacity of the entire calorimeter system. The law of heat exchange states the heat loss by the environment must be equal to the heat gained by the object, or as showed by the equation,

As a form of energy, the SI unit for heat is the joule (J), though heat is frequently also measured in the calorie (cal), which is defined as "the amount of heat required to raise the temperature of one gram of water from 14.5 degrees Celsius to 15.5 degrees Celsius." Heat is also sometimes measured in "British thermal units" or Btu.

          Another thing that is important in using heat and calorimetry is the specific heat. The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius. Specific heat is defined as the amount of heat that has to be transferred to or from one unit of mass or mole of a substance to change its temperature by one degree. Specific heat is a property, which means that it depends on the substance under consideration and its state as specified by its properties. Fuels when burned, release much of the energy in the chemical bonds of their molecules. Upon changing from one phase to another, a pure substance releases or absorbs heat without its temperature changing. The amount of heat transfer during a phase change is known as latent heat and depends primarily on the substance and its state.

The relationship between heat and temperature change is usually 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.

          Calorimeters are designed to be well-insulated, so no heat is gained from or lost to the surroundings. If no heating element is used to introduce heat in the system, the total heat transferred (q) for the entire calorimeter system must equal zero. The total heat can be split into heats for each component in the system. So in this experiment, we are going to find or determine the specific heat of metals, Aluminium Metal and the Copper Metal and see how the latter statement can affect the results of the experiment. We are also going to determine the latent heat of fusion of ice.

          To start the experiment, materials were first given to us. The materials used were: 1 piece of electric stove, 1 piece of calorimeter, 2 pcs of thermometer, 1 pc copper metal, 1 pc aluminium metal, 1 pc beaker, 1 set of weights, 1 piece digital weighing scale and a cup of ice.

          Experiment 2 is all about heat and calorimeter. Here we are required to evaluate the specific heat of metal and latent heat of fusion of ice by means of using the calorimeter as equipment for the experiment. The experiment has 2 parts, the first part is for the specific heat of metal and the second part is the latent heat of fusion of ice.

In the first part, 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. Using the formula,

For aluminium:

The derivation of the formula can be found at the end part of the analysis. As seen in the table, there is a 10.80% error for having an experimental value of 0.2409 cal/g-ºC compared to the actual value of specific heat of aluminum metal of 0.2174 cal/g-ºC.

For copper:

There is a 10.99% error for having an experimental value of 0.1034 cal/g-ºC compared to the actual value of specific heat of copper metal of 0.0932 cal/g-ºC.

 

This percentage of error is acceptable since it is not an isolated system and many factors set in. Therefore it is hard to get an accurate reading.

Possible errors for this are:

Ø The time the metal is immersed in boiling water. Errors can be minimized if we immerse the metal for a long period of time.

Ø The measurement of temperature. It can be minimize be measuring it near the boiling water to avoid the cold air that also affect the experiment.

Ø 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.

The results achieved are shown below:

 

 

Part 1, Determining the Specific Heat of Metals
	Trial 1. Aluminum Metal	Trial 2. Copper Metal
Mass of metal,	45 g	20 g
Mass of calorimeter,	60.6 g	60.6 g
Mass of water,	200 g	121.3 g
Initial temperature of metal,	90 ºC	94 ºC
Initial temperature of calorimeter,	28 ºC	28 ºC
Initial temperature of water,	28 ºC	28 ºC
Final temperature of mixture,	31 ºC	29 ºC
Experimental specific heat of metal,	0.2409 cal/g-ºC	0.1034 cal/g-ºC
Actual specific heat of metal,	0.2174 cal/g-ºC	0.0932 cal/g-ºC
Percentage of error	10.80 %	10.99 %

In the second part of the experiment, we are required to get the latent heat of fusion of ice. Same in part one 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. Mass of ice is inversely proportional to the latent heat. If mass of ice is greater than its initial, then the latent heat will decrease. We computed the latent heat of fusion and got approximately 9~10% error. Our experimental values were 72.79 cal/g and 71.49 cal/g.  the graph shows how part 2 of this experiment was being made. Temperature changes with time. Phase changes are indicated by flat regions where heat energy used to overcome attractive forces between molecules

Possible errors are:

Ø The room temperature, since we are performing in the laboratory with air conditioned room; it can be minimized by performing the experiment fast and consistent.

Ø The mass of ice before and after putting it in the calorimeter, a sudden change in the mass of ice will result to an error. In able to minimize the error, we must wipe off the excess water in the ice before putting it in the calorimeter.

Ø The measurement of temperature, it can be minimize be measuring it near

Ø the boiling water to avoid the cold air that also affect the experiment.

 

Part 2, Latent Heat of Fusion of Ice
	Trial 1. Aluminum Metal	Trial 2. Copper Metal
Mass of calorimeter,	60.6 g	60.6 g
Mass of water,	163.09 g	166.70 g
Mass of mixture,	189.19 g	186.80 g
Mass of ice,	26.1 g	20.1 g
Initial temperature of ice,	0 ºC	0 ºC
Initial temperature of calorimeter,	28 ºC	28 ºC
Initial temperature of water,	28 ºC	28 ºC
Final temperature of mixture,	15 ºC	18 ºC
Experimental Latent heat of fusion,	72.79 cal/g	71.49 cal/g
Actual specific Latent heat of fusion,	80.00 cal/g	80.00 cal/g
Percentage of error	9.01 %	10.64 %

 

 

 

DERIVATIION OF FORMULA TO FIND SPECIFIC HEAT:

 

Where:

cw	-Specific heat of water	mw	-Mass of water
tmix	-Final temperature of mixture	mcal	-Mass of calorimeter
tw	-Initial temperature of water	mm	-Mass of the metal

 

 

DERIVATION OF FORMULA TO FIND LATENT HEAT OF FUSION:

 

 

 

Where:

cw	-Specific heat of water	mcal	-Mass of calorimeter
tmix	-Final temperature of mixture	mice	-Mass of ice
tw	-Initial temperature of water	tice	-Temperature of ice
mw	-Mass of water	Lf	-Latent heat of fusion of ice

 

 

CONCLUSION ON HEAT AND CALORIMETRY

The objectives of the experiment were 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 concept of 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.

And in performing the experiment we should consider the following factors. One, the place where the experiment will be held for it can affect temperature of each object or mixture. Two, the temperature of the given material, from initial to the final temperature of that specific material must also be given considerations.