Final answer:
The rate of heat transfer where a copper rod touches a plastic rod will be lower in the plastic due to its poorer thermal conductivity, despite both rods having the same dimensions. This difference in thermal conductivity will result in a temperature gradient and a change in the heat flux at the point of contact.
Step-by-step explanation:
When heat is conducted from the hot end of a copper rod to the cold end of a plastic rod, with both rods being of the same length, the rate of heat transfer at the interface where they touch can be influenced by their thermal conductivity. Copper, being a good conductor of heat, will transfer heat at a higher rate compared to plastic, which is a poor conductor. Therefore, at the midpoint where the copper rod meets the plastic rod, there will be a significant difference in the rate of heat transfer due to the discrepancy in their thermal conductivities.
In essence, because copper is a good conductor (as are most metals like aluminum, gold, and silver), it will transfer heat quickly to the point of contact with the plastic. Conversely, since the plastic is a poor conductor (much like wood, rubber, and other insulating materials), the heat will transfer through the plastic rod at a slower rate. This means that heat flow into the plastic will be limited by its lower thermal conductivity. The effect results in a gradient in temperature and heat flux across the connection between the two rods.