Tanner Guerra

Lab Group 4 Module B

ENTROPY OF PHASE CHANGE THERMAL ENERGY STORAGE Keywords: thermal energy storage, Phase Change Materials, heat flow, phase diagram, latent heat of fusion, DSC, MPCM, fatty acids, melting point, thermal stability

 

 

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ABSTRACT In the world today we have many problems, but one of our most substantial

problems is the global energy crisis. It won’t be solved by one solution, rather the sum

of many energy usage innovations. This experiment intended to understand an energy

saving innovation, namely, thermal energy storage (TES) via Latent Heat Storage. Phase

Change Materials (PCMs), used for Latent Heat Storage, were subjected to Differential

Scanning Calorimetry (DSC), to generate thermal profiles (Heat Flow vs. Temperature).

These PCMs were Micro-encapsulated paraffin wax, stearic acid, lauric acid, and binary

mixtures of these acids. DSC determined the PCMs physical properties that convey the

thermal energy storage capacity. Specifically, Specific Heat Capacity (Cp), Melting Point

(Tm), and Latent Heat of Fusion (∆Hm or Lf). DSC aids the assessment of thermal

stability (taking thermal cycle data), as well as enabling the procurement of the solid-

liquid phase diagrams for our acid mixture. The phase diagram, with the obtained

solidus and liquidus lines, presents us with a eutectic reaction. The results realize a

eutectic point for the acid mixture was at the mole fraction (𝛘lauric    = .810 or 75 wt.%

lauric acid in stearic acid). The procured phase diagram with Melting Points and

corresponding Latent Heat of Fusion values along with thermal stability enable the

determination of the adequacy of certain mixtures in thermal energy storage

applications.

 

 

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INTRODUCTION

In thermal energy storage (TES) systems, materials are carefully selected based

on the type of system: Sensible Heat Storage, Thermochemical Storage, or Latent Heat

Storage. In sensible heat storage, energy is stored by changing the temperature of a

storage medium, where specific heat capacity is the relevant thermal property.

Thermochemical Storage involves chemical reactions, typically reactions where the

energy is stored indefinitely in the products at room temperature with no loss of heat

capacity. When the energy is required, these products are recombined in a chemical

reaction where energy is released. With Latent Heat Storage, energy is stored as latent

heat in suitable materials during a phase change. The energy that is absorbed during the

melting process is stored as latent heat of fusion and is released during the freezing

process. The thermal characteristics that are relevant here are the latent heat of

melting/fusion and the melting point of the material. The energy is absorbed/released

in a small temperature range making some of these materials attractive for smaller and

lighter storage devices with low storage losses [1]. For PCMs, the relationship between

Latent Heat of Fusion of (∆𝐻!"#,!) and melting temperature (T), for some pure solid A,

can be related via gas constant (R), mole fraction of A in B (𝜒!), and the melting

temperature of pure A (𝑇!!).

𝑙𝑛(𝜒!) = − ∆!!"#,!!

(!!− !

!!!) (3)

This equation also applies for a substance pure substance B in the mixture, and where

the two curves meet (are equal) is the eutectic temperature (𝑇!) and the eutectic

composition  (𝜒!), which is applied in Figure 1 [3].

 

 

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When selecting a material for TES, it is important to look at, not just melting

temperature, but at Latent Heat of Fusion. Although ∆𝐻!"#,!/∆𝐻! is mentioned above

as a part of the phase diagram, it does not explicitly quantify it. To obtain the value for

∆𝐻!, which aided in executing the phase diagram, the heat flow vs. temperature graph,

shown below in figure 2, from DSC is examined.

Figure 1:Solid-liquid equilibria of a two-component system. A euctectic mixture of Pure A and Pure B, where E is the Eutectic Point at eutectic temperature Te and eutectic composition 𝜒!. Furthermore, 𝑇!! is the melting temp. of pure A and 𝑇!! is the melting temp. of pure B. [3] Figure adopted from Castellan, G. W.

Figure 2: A sketch of a DSC thermogram as provided by the Lab B Handout. Tm is the melting temperature, ∆𝐻! is the latent heat of fusion, while Cp (s) and Cp (l) are the heat capacity at constant pressure in the solid and liquid phase. [1]

 

 

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𝑇! is found by finding the temperature when the peak reaches its max (when there are

multiple peaks we take the T at the max of the last peak, because the last peak is the

peak for the liquidus line, therefore the 𝑇!).  ∆𝐻! is calculated by finding the area under

the peak of the heat flow (seen in the figure above). Lastly, the 𝐶!’s are found before and

after a peak, the value is found via a ratio with a standardized material with known

mass and 𝐶! values (elaborated on in data analysis).

EXPERIMENTAL PROCEDURE

MATERIALS

INSTRUMENTS

Differential Scanning Calorimeter TA Instruments – Model Q100,

Microbalance, and a Hotplate.

SPECIMEN PREPARATION

Lauric and stearic acid mixtures of certain compositions were pre-made by the

following steps. Weigh the desired amounts of lauric acid and stearic acid of the desired

 

 

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composition to make 100 mg of the mixture. Transfer the mixture into a vial and heat it

on a hotplate until a homogenous solution is formed (T > 69˚C, the melting temperature

of stearic acid). Equilibrate for 10-15 minutes, turn off the hotplate, and cool the solution

to room temperature [1].

Weigh 2 – 8 mg (preferably 3 – 5 mg [Singh]) of the PCM on the microbalance

and put it in an aluminum pan and spread evenly to ensure proper thermal contact,

then crimp the pan with the lid [1].

DIFFERENTIAL SCANNING CALORIMETRY (DSC)

DSC [19] measures the temperature and the heat flow corresponding to the

thermal performance of materials, both as a function of time and temperature. TA

Instruments DSC is a system which the differential heat flux between a reference (a

sealed empty aluminum pan) and a sample (in a similar pan) is measured. The

reference and the sample pans are placed on adjacent, identical stages on a

thermoelectric sensor platform encircled by a furnace. As the temperature of the furnace

is changed (heating linearly), heat is transferred to the sample and reference through

the thermoelectric platform. The Q100 calculates the heat flow difference between the

sample and the by measuring the temperature difference between them by using

thermocouples attached to the each stage. A peak in heat flow represents a phase

transition, thermal values can then be calculated off of the graph as previously

explained [19].

 

 

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DSC MEASUREMENTS [19, 1]

Record a baseline thermal profile with empty, equal mass aluminum pans placed

on the reference and the sample stages, respectively. The aluminum pan on the

reference stage must be crimped. The pan on the sample stage is left uncrimped for later

use. The baseline scan corrects for any asymmetry in the heat flow to the 2 stages [1].

Obtain a thermal profile with a calibration standard (sapphire) using the same scan

conditions as above. Provide a calibration factor that translates the measured heat flow

units �(in mW) to heat capacity units (in J/g˚C). Place the crimped pan containing the

calibration standard (sapphire, mass = 25.74 mg) on the sample stage [1].

Obtain thermal profiles for each sample using same scan conditions, then enter the

weighed amount for each sample in units of in (mg). Clean the pans before placing on

them on the sample stage. Once done collecting the data must be subtracted by the

baseline data from the sample and sapphire data.

After the baseline, leave the pan on the reference stage undisturbed for the remaining measurements [lab].

 

 

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ANALYSIS/RESULTS

SPECIFIC HEAT CAPACITY

The values of Cp for our PCMs were calculated in excel (& lab notebook) given

the data from DSC. The equation used is:

Where is a calibration factor

obtained from the sapphire standard values. Calculated Cp’s for specific temperatures

is in figure 3, below.

 

We see that Cp increases with temperature, which holds true because of the increased

degrees of freedom that are related to an increase in temperature.

PHASE DIAGRAM

Using the peak fitting software, we obtained values for temperature at different

phase transitions. The calculations and subsequent conversion to mole fraction for

composition are in Table 1 below.

0.000  

0.500  

1.000  

1.500  

2.000  

2.500  

3.000  

0   0.2   0.4   0.6   0.8   1  

Cp  (T)  [J/g*C]  

Acid  Mixture  Composition  %  wt  Lauric  

Cp  (T)  as  related  to  Compostion  of  Acid  Mixture  

Cp(80°C)  [J/g°C]  

Cp(60°C)  [J/g°C]  

Cp(20°C)  [J/g°C]  

Figure 3: Graph of the heat capacity for constant pressure as it varies with % wt. of lauric acid and varying temperatures.

 

 

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The values in the table present the idea that this is not a binary system, because if it

were a binary system, we would only have a max of two peaks, or a Solidus and

liquidus line only. Our data is shown in Figure 4, the phase diagram below.

Fatty  Acid  Samples   T,  Solidus   T,  Intermediate,  1   T,  Intermediate,  2   T,  Liquidus  (Compositions  in  mole  fraction)  

                       100%  Stearic  Acid               71.3   0  

90%  Stearic,  10%  Lauric  Acid   34.8   38.9       68.3   0.136  

80%  Stearic,  20%  Lauric   38.9   41.2       64.8   0.262  70%  Stearic,  30%  Lauric   37.8   41.9       64.4   0.378  

60%  Stearic,  40%  Lauric   40   42.9       58.8   0.486  50%  Stearic,  50%  Lauric   39.5   44.3   50.2   55.4   0.587  

40%  Stearic,  60%  Lauric   40.6           44.1   0.681  30%  Stearic,  70%  Lauric   40.8           44.3   0.768  

25%  Stearic,  75%  Lauric   42.2           42.2   0.810  

20%  Stearic,  80%  Lauric               41.5   0.850  10%  Stearic,  90%  Lauric   40.1           42.9   0.927  

100%  Lauric               46.8   1  

Table 1: Values to help graph the phase diagram for the fatty acid mixture, which will have each T value as related to the composition in mole fraction.

0  

10  

20  

30  

40  

50  

60  

70  

80  

0   0.2   0.4   0.6   0.8   1  

Temperature  (C)  

Mole  Fraction  of  Lauric  Acid    

Phase  Change  Diagram  for  Fatty  Acids  

T,  Liquidus  

T,  Intermediate  1  

T,  Intermediate  2  

T,  Solidus  

Figure 4: The phase diagram of the eutectic mixture of Lauric Acid and Stearic Acid.

 

 

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It is clear that the Eutectic Point lies at the Mol fraction value of .810 (75% wt Lauric),

which is also evident in Table 1.

This is an unlikely mixture to be applied in household energy saving products because

it has a eutectic point at around 42*C, much too hot to be applicable anywhere where

people are at.

Below are the experimental and literature values for Lab B, I am currently running out

of time, otherwise I would explain further in detail the implications of these results.

Material   Tm  exp  [°C]  Tm  literature  

Latent  Heat  (J/g)  

Latent  Heat  -­‐  literature  

Mass  [mg]   Mass  [g]   Qrev  [J]   DS  [J/K]  

MPCM  18D   18.7   18   182.1                                                163-­‐173   3.8   0.0038   0.692   0.037  

MPCM  28D   28.7   28   190.8                                                      180-­‐195   3.6   0.0036   0.687   0.0239  

Tempertex   27.6       19.24       3.7   0.0037   0.0712   0.00258  Unknown   55.2       206.7       3.2   0.0032   0.661   0.012  100%  Stearic   71.3   67.2   232.3   198.9   2.9   0.0029   0.674   0.00945  90%  Stearic,  10%  Lauric   68.3   67.8   214.2       5.18   0.00518   1.11   0.0163  80%  Stearic,  20%  Lauric   64.8   65.1   229.2       2.3   0.0023   0.527   0.00813  70%  Stearic,  30%  Lauric   64.4   62.4   203.6       4.74   0.00474   0.965   0.015  60%  Stearic,  40%  Lauric   58.8   59.4   203.1       4.1   0.0041   0.833   0.0142  50%  Stearic,  50%  Lauric   55.4   55.9   193.8       4.8   0.0048   0.93   0.0168  40%  Stearic,  60%  Lauric   44.1   33.8–47.6   193.2   189.8   4.4   0.0044   0.85   0.0193  30%  Stearic,  70%  Lauric   44.3   35.9–42.7   187.1   187.1   4.84   0.00484   0.906   0.0205  25%  Stearic,  75%  Lauric   42.2   36.9–37.6   177.7   183.4   4.8   0.0048   0.853   0.0202  20%  Stearic,  80%  Lauric   41.5   38.2–33.7   183.6   180.5   6.01   0.00601   1.1   0.0265  10%  Stearic,  90%  Lauric   42.9   41.7   173.8       4.6   0.0046   0.799   0.0186  100%  Lauric   46.8   42.4   210   186.4   4.4   0.0044   0.924   0.0197  

Table  2:  The  red  data  is  most  likely  a  mass  error,  it  is  unusually  lighter  than  the  rest.  That  value  will  likely  need  to  be  re-­‐done.  

 

 

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REFERENCES

(1) Kimerling, L.; Berera, G.P. 3.014 Module B Handout, 2013.  (2) Costa, M. C., Rolemberg, M. P., Meirelles, A. J. A., Coutinho, J. A. P., & Kraehenbuehl, M. A. (2009). The

solid-liquid phase diagrams of binary mixtures of even saturated fatty acids differing by six carbon atoms. Thermochimica Acta, 496, 30–37. doi:10.1016/j.tca.2009.06.018

(3) Castellan, G. W. in Physical Chemistry, 3rd ed. Ch. 13 and 15, The Benjamin/Cummings Company Inc.

(1983).