Thermodynamics – conduction

1. The problem statement, all variables and given/known data
A bar of gold (Au) is in thermal contact with a bar of
silver (Ag) of the same length and area (Fig. P20.39).
One end of the compound bar is maintained at 80.0°C,
and the opposite end is at 30.0°C. When the energy
transfer reaches steady state, what is the temperature at
the junction?

The figure just shows that the two blocks are insulated from all other directions – so ignore conduction to anything else.
2. Relevant equations

P=kA(ΔT)/L

3. The attempt at a solution
If one side is maintained at 80C wouldn’t the whole system just keep warming up until it reaches 80C (steady state) then just conduct the same amount of heat that comes in from one side to the other side?

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