1.10. The van der Waals equation of state is P=kBT/(vb)a/2, where a and b are constants. This equation describes both a liquid and vapor phase, and therefore produces a vapor-liquid phase envelope. (a) At constant temperature, there is a single equilibrium P,vG, and vL. Write three algebraic equations that can be solved simultaneously to give these values for a given T. (b) Write an equation that can be solved to determine the spinodal volume, vspin. Explain how the resultant equation can give both vG,spin and vL,spin. (c) Find the critical temperature Tc, volume vc, and pressure Pc in terms of the constants a and b