What were the stages of technology development?

The thermal expansion or contraction of a given metal is a function of the f a)-density b)-initial temperature c)- temperature difference d)- linear coefficient of thermal expansion e)- final temperature f)- original length

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.

What is the heat treatment of metals? what is the benefit of it? why and how it's useful? answer in details, do not write by hand.