Starting with one-dimensional steady-state energy equation with constant thermal conductivity, k, derive expressions step-by-step for temperature distribution, heat flux, and heat transfer rate in a hollow sphere when the inner and outer radii are r1, and r2 and the temperatures are t, and t2, respectively.

Describe one experiment in which the glass transition temperature and melting temperature of a totally amorphous thermoplastic material can be determined. show the relevant experimental results in a diagram which should be properly annotated with the two temperatures clearly marked. what is likely to happen to the curve in the diagram if the amorphous polymer is replaced by a thermosetting type?