Ardan_ina_physics_latentheatoffusion.docx

Latent Heat of Fusion Ina Ardan

Abstract: Latent heat of fusion is the energy required to change the phase of a substance from liquid to solid and vice versa. It is also the difference in the internal energy of a substance when it changes from one phase to another, which means that it requires the mass, specific heat and change in temperature of the substance. The experiment aims to determine the latent heat of fusion of water. The formula for the latent heat of fusion of water was derived from the formula for heat energy and the formula for heat energy used in the phase change of a substance. The experiment revealed that there are factors that could affect the data required to determine the latent heat of fusion of water, such as the heat energy absorbed by the calorimeter and the surrounding air. Nonetheless, it was concluded in the end that substances or materials with high latent heat of fusion tend to absorb more thermal energy in a system, thus making them good coolants.

Key Terms: Latent Heat of Fusion; Internal Energy; Phase Change

1. INTRODUCTION 1.1 Describing Latent Heat of Fusion Latent heat of fusion may be defined as the difference in internal energy of a substance when it changes its state from liquid to solid and vice versa. [1] A definition of internal energy is the energy associated with the random, disordered motion of molecules. [2]

Fig. 1.

The physical states of water

For example, steam has higher internal energy than water, and water has higher internal than ice because the molecules of the former are more scattered or in greater motion than the latter, as seen in fig. 1. Molecules of substances with higher internal energy experience weaker intermolecular forces than those with lower internal energy. It takes a certain amount of energy to bring molecules closer or farther from each other. This leads us to the concept of latent heat as the energy used to change the molecular configuration of a substance. [3]

1.2

Uses of Latent Heat of Fusion

It is also stated that heat of fusion is the energy required to change a gram of a substance from the solid to the liquid state, or vice versa, without changing its temperature. [4] With this information, the substances that will absorb and release energy can be determined. In the experiment, the substance that absorbed heat is ice while the substance that released heat is the warm water. This is because ice requires less energy to change its phase from solid to liquid.

2. THEORY 2.1 Heat Energy In a system where two substances have different temperature, heat will continue to be transferred until they reach a point of thermal equilibrium. [5] When a substance gains or loses heat energy without a phase change, the formula is:

Q=mCΔT

(Eq. 1)

where: Q = heat energy (in Joules or calories) m = mass of the substance (in grams) C = specific heat of the substance (in units of J/g °C or cal/g °C), and ∆T = difference between starting and ending temperatures (in °C).

When a phase change happens, the formula is:

Q=m Lfus

(Eq. 2)

where: Lfus = heat of fusion

2.2 Equation of Latent Heat of Fusion The heat energy released by a substance should be equal to heat energy absorbed by the other substance it is in thermal contact with in the system. [1] In the case of substances with different states, for example, in the case of ice and warm water where the ice and solid and the warm water is liquid, the heat energy released by the warm water (Q lost by warm water) is equal to the heat energy gained by the ice (Q gained by the ice ) and the heat energy required to change the phase of ice (Qfusion).

Qlost by warm water =Q gained by ice +Qfusion

(Eq. 3)

Equations 1 and 2 will then be substituted into equation 3, and by manipulation of variables, the formula for latent heat of fusion (Lf) may be derived.

mwater

( 1gCcal° ) (T

initial

−T final )=mice

(T ( 1cal gC ° )

final

−T initial ) + mice L fus

The change in temperature for the warm water is set as initial temperature minus the final temperature, and final temperature minus initial temperature for ice to yield a positive value for both.

( T −T ( 1gCcal° ) (T −T )−m ( 1cal gC ° ) ( 1gCcal° )( T −T )−m ( 1gCcal° ) (T −T )

mice Lfusion =mwater m water Lfusion =

initial

initial

final

final

initial

ice

ice

final

final

)

initial

mice (Eq. 4)

3. METHODOLOGY 3.1 Procedure For this experiment, the researcher/s will need a calorimeter, thermometer, weighing scale, warm water and ice (at melting point). Start by determining the temperature of ice, which should be 0˚C, its melting point, and the room temperature for reference, using the thermometer. Get the mass of the empty calorimeter using the weighing scale, then fill it up to about half full of warm water. Weigh the warm water with the calorimeter and get the mass of the warm water by using:

mwater =mcalorimeter with water−mempty calorimeter Determine the temperature of the warm, water using the thermometer then start adding the ice chunks, wiping off the excess water before putting it into the calorimeter. Stir until all the ice has melted, then get the final temperature (Tfinal). Immediately after measuring the final temperature, measure the final mass (mfinal), then get the mass of ice using:

mice=mfinal −mwater

Fig. 2.

Stirring the water with ice

Fig. 3.

Measuring the temperature of the water after all the ice has melted

With all the data gathered, the latent heat of fusion per gram of water can be determined using eq. 4. (see eq. 4)

4. DATA AND RESULTS 4.1 Results of Experiment The room temperature, mass of calorimeter, mass of calorimeter with warm water, initial temperature of warm water and the final temperature and mass of the water were recorded in table 1. With the available data, the mass of warm water and mass of ice were computed and also recorded in table 1. Variables Room Temperature Mass of calorimeter, mcalorimeter (g) Mass of calorimeter plus warm water, mcalorimeter with water (g) Mass of warm water, mwater (g) Initial temperature of warm water, Tinitial (˚C) Final temperature, Tfinal (˚C) Final mass, mfinal (g) Mass of ice, mice (g) Table 1 Data Table

Data 24. 5 15 g 224 g 209 g 77 ˚C 28 ˚C 308 g 84 g

The gathered will then be plugged into equation 4, noting that the initial temperature of ice is 0 ˚C, its melting point.

m water Lfusion =

( 209 g ) ¿

(T ( 1gcal °C )

initial

−T final )−mice

(T ( 1g cal °C)

final

−T initial )

mice 1 cal ( 77 ° C−28 ° C ) −( 84 g ) ( ( 28° C−0 ° C ) ( 1cal g°C ) g°C )

( 84 g )

≈ 94 calories The standard latent heat for water is 79.7 calories.

Percent error=

[5]

Determine the percentage error by using:

Experimental value−Standard Value ×100 Standard Value (Eq. 5)

¿ ≈

94 calories−79.7 calories × 100 79.7 calories 18%

5. ANALYSIS AND DISCUSSION 5.1 Data Analysis The data from the experiment reveals that the substance with lower internal energy will absorb more heat energy than the substance with higher internal energy. The data also shows that it took an estimate of 94 calories to melt 84g of ice. However, the standard value is 79.7 ˚C, which means that there were errors during the data collection.

5.2 Reasons for Error The heat energy that could have been absorbed by the air and the calorimeter were not taken into consideration in the equation. Another possible error would be that the excess water on the pieces of ice added into the calorimeter were not properly wiped off. It could also be that the water may not have been stirred properly, making the temperature unequal; thus, the final temperature measured may be inaccurate. These errors could be considered as personal error since they may have been prevented if the procedures were more properly followed. Lastly, there may be instrumental error, such as the accuracy of the data given by the weighing scale.

6. CONCLUSION By determining the heat of energy of substances that will be put into a system, the substances that will release and absorb heat may be identified. A material with a higher latent heat of fusion will require more energy to change its phase. These materials or substances make good coolants because they prevent the other substance within the system from absorbing heat energy by absorbing heat energy first.

7. ACKNOWLEDGEMENTS

The researcher would like to acknowledge De La Salle University for allowing the use of the physics lab and providing the needed materials for the experiment.

The researcher would also like to thank former and present physics professors for contributing to the researcher’s understanding of the concepts used in the experiment and in the report.

8. REFERENCES [1]

De La Salle University Physics Department, "Undergraduate Laboratory Experiments," [Online]. Available: https://www.dlsu.edu.ph/academics/colleges/cos/physics/_pdf/cos-heat-of-fusion.pdf.

[2]

R. Nave, "Internal Energy," HyperPhysics, 2001. [Online]. Available: http://hyperphysics.phyastr.gsu.edu/hbase/thermo/inteng.html.

[3]

D. M. C. D. Galves, "Undergraduate Laboratory Experiements," 2012. [Online]. Available: https://www.dlsu.edu.ph/academics/colleges/cos/physics/_pdf/cos-Activity5-heat-of-fusion%28secured%29.pdf.

[4]

"What is Enthalpy or Heat of Fusion?," innovateus, 2013. [Online]. Available: http://www.innovateus.net/science/what-enthalpy-or-heat-fusion.

[5]

The Editors of Encyclopædia Britannica, "Latent Heat of Fusion," Britannica , 2016. [Online]. Available: https://www.britannica.com/science/latent-heat.