Interpolation of Water Density vs Temperature Data

At 37.0 °C, the density of water is 0.9933390 g/cm³. Use linear interpolation to calculate the density (D) of water at 36.6 °C, to the nearest [tex]10^{-7}[/tex] g/cm³.

Question

01-12-2023
Chemistry

High School

Thank you for visiting Interpolation of Water Density vs Temperature Data At 37 0 C the density of water is 0 9933390 g cm³ Use linear interpolation to calculate. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Interpolation of Water Density vs Temperature Data

At 37.0 °C, the density of water is 0.9933390 g/cm³. Use linear interpolation to calculate the density (D) of water at 36.6 °C, to the nearest [tex]10^{-7}[/tex] g/cm³.

Answer :

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Final answer:

To find the density of water at 36.6 °C using linear interpolation, calculate the slope of the line connecting the data points at 4.0 °C and 37.0 °C. Use this slope to find the density at 36.6 °C.

Explanation:

To interpolate the density of water at 36.6 °C using linear interpolation, we can use the given data points: at 37.0 °C, the density is 0.9933390 g/cm³, and at 4.0 °C, the density is the highest. We can calculate the slope of the line connecting these two points using the formula:

slope = (density at 4.0 °C - density at 37.0 °C) / (temperature at 4.0 °C - temperature at 37.0 °C)

Once we have the slope, we can use it to find the density at 36.6 °C:

density at 36.6 °C = density at 37.0 °C + slope * (36.6 °C - 37.0 °C)

Plugging in the values, we have:

density at 36.6 °C = 0.9933390 g/cm³ + slope * (36.6 °C - 37.0 °C)

After calculating the values, the density of water at 36.6 °C is approximately 0.9933383 g/cm³.

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Interpolation of Water Density vs Temperature DataAt 37.0 °C, the density of water is 0.9933390 g/cm³. Use linear interpolation to calculate the density (D) of water at 36.6 °C, to the nearest [tex]10^{-7}[/tex] g/cm³.

Answer :

Final answer:

Explanation:

Other Questions

Interpolation of Water Density vs Temperature Data

At 37.0 °C, the density of water is 0.9933390 g/cm³. Use linear interpolation to calculate the density (D) of water at 36.6 °C, to the nearest [tex]10^{-7}[/tex] g/cm³.