By: Tao Steven Zheng (郑涛)

【Problem】

Consider two slabs of lengths and , and cross-sectional area . The respective thermal conductivity constants are and .  

Part 1: Based on the below diagram, the temperature on the left is hotter than the temperature on the right () calculate the temperature between the two slabs .

Part 2: Calculate if and .

【Solution】

Part 1

Heat naturally flows from higher temperature to lower temperature. Based on the diagram, the heat flows at a rate from left to right.

Thus,

Consequently,

Part 2

If and ,

becomes

Factoring out yields