2. Peng-Robinson Equation of State The Peng-Robinson equation of state has the following form: \[ p=\frac{R T}{v-b}-\frac{a}{v^{2}+2 b v-b^{2}} \] where \( a, b \) are constants. a) Sketch a few isotherms on the pv-plane of a Peng-Robinson substance. b) Find the compressibility of this substance. c) Find the first three virial coefficients of the Peng-Robinson substance.