# linear interpolation

• Feb 19th 2009, 07:13 AM
VkL
linear interpolation
PV^K=C (K and C are constants)

P(mmHg) 760 -- 1140 -- 1520 -- 2280 -- 3040 -- 3800
V(cm^3) 48.3 -- 37.4 -- 31.3 -- 24.1 -- 20.0 -- 17.4

Determine the values of K and C that fit the data best (Include units)

This has something to do with the power law... can anybody help?
• Feb 19th 2009, 07:57 AM
HallsofIvy
Quote:

Originally Posted by VkL
PV^K=C (K and C are constants)

P(mmHg) 760 -- 1140 -- 1520 -- 2280 -- 3040 -- 3800
V(cm^3) 48.3 -- 37.4 -- 31.3 -- 24.1 -- 20.0 -- 17.4

Determine the values of K and C that fit the data best (Include units)

This has something to do with the power law... can anybody help?

Take the logarithm of both sides of PV^K= C. You get log(p)+ Klog(V)= log(C) which is a linear equation. Take the logarithms of P and V to get new data. Use "least squares"
http://www.ltcconline.net/greenl/cou...astSquares.htm
to get the line that best fits that data. That will be an equation of the form y= ax+ b. If you use log(V) as "x" and log(P) as "y" that will correspond to log(P)= -Klog(v)+ log(C) so K= -a and \$\displaystyle C= e^b\$.