Linear Interpolation: Given a pair of (x1,y1), (x2,y2) and x3 predict (x3,y3)

02142014, 02:52 PM
(This post was last modified: 02142014 04:11 PM by Han.)
Post: #2




RE: Linear Interpolation: Given a pair of (x1,y1), (x2,y2) and x3 predict (x3,y3)
In general your interpolation (and its accuracy) depends on the relationship between the parameters. For your example, if you use \( PV=nRT \) and pressure \( P \) is kept constant, then in this case a linear interpolation would be fine since
\[ V = \underbrace{\frac{nR}{P}}_{\text{slope}} \cdot T \] So since \( n \), \( R \) and \( P \) are constant, then \( V \) is a linear function of \( T \). This should enable you to interpolate the volume provided the pressure is fixed at 100k pascals. Haven't tested this, but using a linear fit with your known values and then using the trace feature should allow you to figure out the interpolated volume. Graph 3D  QPI  SolveSys 

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