1. What is Linear Interpolation?

Linear interpolation is a method of estimating unknown values between two known data points. It assumes the change between the points is linear and calculates intermediate values accordingly.

2. How Does the Calculator Work?

The calculator uses the linear interpolation formula:

Where:

• \( (x_1, y_1) \) — First known point
• \( (x_2, y_2) \) — Second known point
• \( x \) — Desired x value between x1 and x2
• \( y \) — Calculated y value at x

Explanation: The formula calculates the slope between two points and applies it to find the y-value at any intermediate x-value.

3. Importance of Linear Interpolation

Details: Linear interpolation is widely used in thermodynamics, engineering, and data analysis to estimate values between measured data points when the relationship is approximately linear.

4. Using the Calculator

Tips: Enter two known (x,y) points and the desired x value where you want to estimate y. The x value must be between x1 and x2 for proper interpolation.

5. Frequently Asked Questions (FAQ)

Q1: When is linear interpolation appropriate?
A: When the relationship between variables is known to be linear or approximately linear over small intervals.

Q2: What are the limitations of linear interpolation?
A: It can be inaccurate for non-linear relationships or over large intervals between points.

Q3: Can I use this for extrapolation?
A: This calculator is designed for interpolation. Extrapolation (estimating outside the known range) is less reliable.

Q4: How accurate is linear interpolation?
A: Accuracy depends on how close the true relationship is to linear between your known points.

Q5: What are some thermodynamic applications?
A: Estimating properties like enthalpy or entropy at intermediate temperatures from tabulated data.