What do you do if you need a value from a data table that is between two table values?

What is interpolation?

Can you name any types of interpolation besides linear?

What is double interpolation?

Linear Interpolation

Properties of Saturated Steam: Temperature Table

\[\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\]

\[y=\frac{y_2-y_1}{x_2-x_1}({x-x_1})+y_1\]

\[\hat{V}=\frac{\hat{V}_2-\hat{V}_1}{T_2-T_1}({T-T_1})+\hat{V}_1\]

\[\hat{V}=\frac{106.3-120.8}{10-8}({9-8})+120.8=113.55\]

Double Linear Interpolation

What if you’re between values in two dimensions

\(T=125\ \mathrm{^\circ C}\)

\(P=0.3\ \mathrm{bar}\)

\(\hat{V}=?\)

Double Linear Interpolation

Called double interpolation
Have to do three

The Takeaways

Linear interpolation is often used in tables.
Remember \(slope = slope\) to write formula.
A one-dimensional table requires one interpolation.
A two-dimensional table requires double interpolation, which is really three interpolations.

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The Just The Facts companion video is in the link in the upper left. The next video in the series is in the upper right. To learn more about Chemical and Thermal Processes, visit the website linked in the description to find previous and following videos in this series.

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Thanks for watching!
The Full Story companion video is in the link in the upper left. The next video in the series is in the upper right. To learn more about Chemical and Thermal Processes, visit the website linked in the description to find previous and following videos in this series.

The DOFPro Team