A thin long wire is made of a material that undergoes a phase transition so that its resistivity takes one of the two values, p, if its temperature is smaller than T, and py = 2p, if the temperature is larger than To. Assume the following: (a) the heat flux per unit length of the wire to the ambient medium is W = a(T - To), where a is a constant, I denotes the temperature of the wire, and To is the ambient temperature (To > VA. The voltage V applied to the ends of the wire is increased very slowly, at a constant rate (i.e. linearly in time), from zero until the whole wire has undergone a phase transition, and then reduced back to zero, at the same constant rate. Sketch how the total power P dissipated in the wire depends on time t. Your sketch should show power and voltage values at any point where either P or its time derivative is discontinuous, expressed in terms of Po = ol(To - To) and Vo = Lvapi (To - To)/ A. The solution is considered to be correct only if all these points have correct values, and all segments of the graph are qualitatively correct (e.g. a convex curve should not be drawn as a straight line)