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Long time reader first time poster.

I have a problem that I am trying to solve below.

**Problem 1**

A metal copper rod say 20mm diameter has a constant heat applied to it of 150°C on one end. Ambient temp of Air is 25°C.

What length rod do I need so the other end is at 50°C one equilibrium is reached?

**Problem 2**

Also another one that I am looking at is. If the electric stove hot plate is at a constant 100°C area of 100mmX100mm what would be the temperature of the air 200mm above the hot plate using ambient air temp of 25°C again?

They seem like straight forward problems but for the life of me I can't get my head around it. Any help would be appreciate it.

Thank you in advance.