https://file.aiquickdraw.com/mathbot/file/1721117153734ychvom5m.jpg

To determine the percent crystallinity of the PET sample, we can use the provided equation:

\[
\% \text{ Crystallinity} = \left(\frac{\Delta H_m - \Delta H_c}{\Delta H_m^0}\right) \times 100\%
\]

where:
- \(\Delta H_m\) is the heat of melting,
- \(\Delta H_c\) is the heat of cold crystallization,
- \(\Delta H_m^0\) is the heat of melting if the polymer were 100% crystalline.

From the provided graph:
- \(\Delta H_m\) (heat of melting) is 148.86 J/g.
- \(\Delta H_c\) (heat of cold crystallization) is 37.59 J/g.
- \(\Delta H_m^0\) (reference heat of melting) is 140.1 J/g.

Plugging in these values into the equation:

\[
\% \text{ Crystallinity} = \left(\frac{148.86 \, \text{J/g} - 37.59 \, \text{J/g}}{140.1 \, \text{J/g}}\right) \times 100\%
\]

Let's calculate the value:

\[
\% \text{ Crystallinity} = \left(\frac{148.86 - 37.59}{140.1}\right) \times 100\%
\]

\[
\% \text{ Crystallinity} = \left(\frac{111.27}{140.1}\right) \times 100\%
\]

\[
\% \text{ Crystallinity} = 0.7943 \times 100\%
\]

\[
\% \text{ Crystallinity} = 79.43\%
\]

Thus, the percent crystallinity of the PET sample is approximately 79.43%.

Do you want more details or have any questions? Here are 5 questions you might want to ask:

1. How is the heat of melting (\(\Delta H_m\)) determined from the graph?
2. What is the significance of the heat of cold crystallization (\(\Delta H_c\))?
3. How is the reference heat of melting (\(\Delta H_m^0\)) established?
4. Can you explain the physical meaning of crystallinity in polymers?
5. How does crystallinity affect the properties of PET?

**Tip:** When interpreting thermograms, always pay attention to the onset and peak temperatures, as they indicate important transitions in the material's thermal behavior.

Learn how to calculate the percent crystallinity of a PET sample using thermodynamic data. Includes step-by-step calculation using the heat of melting, heat of cold crystallization, and reference heat of melting. Useful information for students and researchers in polymer science.

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