A thin long wire is made of a material that undergoes a phase transition so that its resistivity takes one of the two values, pl if its temperature is smaller than Tm and p2 = 2,01 if the temperature is larger than Tc. Assume the following: (a) the heat flux per unit length of the wire to the ambient medium is IV = 05(T To), where a is a constant, T denotes the temperature of the wire, and To is the ambient temperature [To > #1. The voltage V applied to the ends of the wire is increased very slowly, at a constant rate (Le. 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 P0 = aLfTC To) and V0 2 L 0501'ch TOMA. 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}