in seeking to find "kv"("v"), one should not unthinkingly eliminate "t" between (4) and (5), since "p" is varying in the former while it is assumed constant in the latter. rather, it should first be determined in what sense these equations are compatible with one another. to gain insight into this, recall that any two variables determine the third. choosing "p" and "v" to be independent, we picture the "t" values forming a surface above the "pv"-plane. a definite "v"0 and "p"0 define a "t"0, a point on that surface. substituting these values in (4) and (5), and rearranging yields