Three states in a thermodynamic process are defined by p1 = 1 bar and v1 = 2 l, p2 = 20 bar and v2 = 0.2 l, and p3 = 4 bar and v3 = 1 l. the quantity β is defined for the path of integration 1-2-3 by: = − ∫ p 2 1 − ∫ p 3 2 determine β (expressed in units of joules) connecting states 1 and 2 with a linear p-v process and connecting states 2 and 3 with a polytropic process. remember that a polytropic process is one that can be described by the following relationship: