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DSC: Heat Capacity and Latent Heat
Objective
The objective of this laboratory is for you to explore the heat capacity of materials due to atomic vibrations and the latent heat of phase transitions, and how these properties can be used to provide storage of thermal energy.
Preparation
Read the chapter from Haines on differential scanning calorimetry and the introductory sections of the review on phase change materials (PCM).
Equipment
- Station for differential scanning calorimetry (DSC)
- Samples of graphite, SiC, paraffin wax, paraffin components (eicosane, tricosane, hexacosane),
bismuth, stearic acid, MgCl 2 ∙6H 2 O
- DSC Al pans and lids, and press for sample prep
- Computer, data - --acqu i s i t i on software, p l ott i ng and analys i s software
Introduction
Knowledge of the heat capacity of materials and the latent heat of phase transitions is necessary to understand the thermodynamics of materials and their phase transitions. For example, for measurements at constant pressure (e.g., in an unsealed container at atmospheric pressure, as in the current experiments), the change in enthalpy is given by the temperature integral of the heat capacity and the change in entropy is given by the temperature integral of the heat capacity divided by temperature. For most solids, at temperatures away from any phase transitions, the vibrations of the atoms control the heat capacity. At a first order phase transition, the latent heat gives the difference in enthalpy and entropy of the two phases.
Heat capacity and latent heat have many practical applications. For example, they are critical to determining the potential of a material for the storage of thermal energy from sunlight. The question in this case is how much heat energy can be stored in a material that is heated by sunlight to a temperature different from ambient by a given amount. Latent heat, for example, is the amount of heat that must be extracted from a volume of water at 0°C to permit it to freeze or which must be put in to a certain amount of ice to make it melt. Both the latent heat and heat capacity can be useful in identifying unknowns or for characterizing components of a mixture.
The heat capacity is the ratio of heat input into an object (for example in Watt seconds) to the temperature increase that results. The calorimeter works by very precisely applying power to the object
(in Watts) and very precisely measuring the temperature change (in Kelvin) per unit time and per unit mass of the object. Because it is convenient to load the sample in a container and because the heat capacity is an “extensive quantity” (i.e. how much heat is required to produce a given temperature change depends on how much material is present), it is convenient to compare the sample in its container to an identical but empty container. The difference represents the heat absorbed by the sample rather than the sample plus the container. By knowing the mass of sample you put in the container, you can determine the specific heat capacity, which is taken per unit mass. Thermodynamically the specific heat capacity is:
𝑐𝑐 =
In other words, it is the change in entropy of the material per unit temperature change multiplied by the temperature per mole of material.
The latent heat represents the change in the internal energy of a solid when passing from one phase to another. This can be a combination of a change in energy (for example , bond energy) and a change in entropy (for example , vibrational or configurational entropy). This value depends upon many factors in a given material. Note that because materials are liquids at higher temperatures than solids, the TS term must favor the liquid because as the temperature increases the entropy terms dominate , and the zero temperature energy of the solid (the bond energy , for example) must favor the solid. Thus, the energy of a solid is lower than the energy of a liquid while the entropy of the liquid is higher than the entropy of the solid.
Finally, note that if you supply heat to a solid at a constant rate then you would expect to see a linear increase in temperature if the specific heat capacity were constant and no phase transition was occurring. In your report for this laboratory determine the heat capacity for t h e specific materials (see below) as a function of temperature for each material from the relationship of heat flow to temperature (the derivative dQ/dT). Discuss the implication for relative dependences of entropy on temperature for different materials (why one material m i g h t have a different entropy compared to another).
If you measure the heat flow into a materia l during a phase change you w ill find heat flowing in at a constant temperature dur i ng me l t i ng and heat f l ow i ng out of the materia l at constant temperature dur i ng freez i ng. The amount of heat absorbed would be the area under the peak i n heat f l ow re l at i ve to the we ll - --behaved (at l east sort of) background due to the heat capac i ty of the sol i d. In your report, account for the heat capacity of the solid (it may change from one phase to another) as best you can and then estimate the amount of heat absorbed or given off in the phase change. This should be the latent heat. Compare your value with the literature.
If you observe any of the following behaviors please explain them as much as possible: (1): a change in the heat flow vs. temperature plot from the first cycle to following cycles, (2) the nature of any second peak you observe that is not the main melting/freezing phase transformation (if any) – you need not explain the origin of this peak but note the latent heat associated with it.
When you measure the heat flow as a function of temperature you may find hysteresis between the two peaks (freezing and melting) when you cycle the temperature of the calorimeter through the phase
- Under the Initial State tab, change the Initial Temp to a value appropriate for your experiment. We will discuss this in lab. Leave the Y initial at 20.00 mW.
- In the Program tab, tailor your program to obtain the desired data. Typ i cal l y, you w ill want to beg i n w i th a 2 -minute i sotherma l hold, and then beg i n heat i ng. M i nimum and max i mum temperatures for the DSC units are - -- 120 and 450°C, respectively. The range of heat i ng and coo li ng rates is 5--- 100°C/m i nute.
- Remove the inner and outer lids of the DSC using tweezers. Make sure a reference pan is present in the furnace. Add the sample pan, making sure the sample pan is centered on the small circular platform. Replace the inner and outer lids. Make sure the nitrogen gas is turned on before you start heating the sample.
- If everything is set the way you want it, click to start the run.
Analysis of heat capacity data
- To determine heat capacity of a material on this DSC, you must first perform a baseline run. A baseline run will determine the small errors in the differential measurements of the heat capacity of the system (furnace, pans, air, etc.) and will be subtracted from the sample data. Place an uncrimped, empty pan and lid in the furnace, along with a (crimped) reference pan.
- Us i ng the Method Ed i tor, set up your program exactly how you p l an on setting up the samp l e program. Save the method f il e by c li ck i ng F il e---> Save Method As and se l ect i ng your group’s fo l der. G i ve the f il e a name such as “Graph i te - --base li ne” and save. Then, run the program.
- After the program has run, take out the empty pan and li d and we i gh 10 - -- 20 mg of mater i al i nto the pan. P l ace the li d on, crimp the samp l e and p l ace i t back i n the DSC. Execute exactly the same program, but add the samp l e mass and change the f il e name.
- After your sample program has run, a Data Analysis window should be open with your data curve. In the upper toolbar, click the Add Curve button ( ) and add your baseline data.
- With the samp l e data curve h i gh li ghted, go to Math - --> Subtract and c li ck the base li ne curve. The resu l t i ng curve i s the data for just the mater i al.
- Cl i ck Ca l c - --> De l ta Y. Change the X l ocat i on of the r i ght li m i t to the temperature at wh i ch you want to know the heat capac i ty.
- Calculate the heat capacity using C (^) p = ΔY/(m β), where m is the mass of the sample in milligrams and β is the heating rate of the sample in degrees C per second.
- Save your data f il e. A l so, c li ck Fil e - --> Export Data - --> ASCII format and save. Th i s w ill create a. txt fi l e that can be opened w i th any spreadsheet program.
Analysis of latent heat data
- No baseline is required for latent heat measurements. We i gh 10 - -- 20 mg of material into an empty pan. Place
the li d on top, cr i mp and p l ace i n the DSC along w i th a reference pan.
- In the Method Editor – Sample Info tab, insert sample info as before. For latent heat analysis, heating runs should begin about 50°C below the melting point of the material, hold at that temperature for 2 minutes, and then begin heating. Heating should continue to 50°C above the melting temperature, and then hold again for 2 minutes. For best results, cool the sample at the same rate as heating, again to 50°C below the melting point.
- One curve w ill be present after data acqu i s i t i on i s comp l ete, but on l y one section can be ana l yzed at a time. Save your data file before analyzing. Go to Curves -> Heat Flow, and select either the heating or the cooling section of the curve. C li ck Ca l c - --> Peak Area. Change the l eft and r i ght li m i ts to a po i nt on either s i de of the endo/exotherm i c peak. Choose these po i nts such that they li e on a flat portion of the curve, before the peak. Check the onset and end boxes, and i f the mo l ar mass is known, check the kJ/mole box and insert the value.
- Cl i ck Curves - --> Heat Fl ow, and se l ect the other curve for analys i s. Remove the f i rst curve and repeat the process.
- When finished, load both curves back onto the plot and export to ASCII data.
Shut down When you are done using the DSC for the day, exit out of Pyris Manager and tell the TA. Do not turn off the DSC, intercooler, or gas regulator. Transfer all of your ASCII files and any screen shots or other files either onto a USB memory stick or via email, Box, Google Docs, etc. Take your sample out of the DSC and place it in the provided sample trash bin.
