# Thermal Conductance Through Two Materials

## Main Question or Discussion Point

I had a thermal conductance homework problem where heat flowed through gold, and then silver. Both materials were of the same length and same cross sectional area. The problem mentioned that the energy transfer had reached a steady state, and I found through doing the problem that under these conditions, conductance would be the same through both materials.

Can anyone explain why this is? I thought that the conductivity of the material would still play a role in the rate of energy transfer.

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mfb
Mentor
I thought that the conductivity of the material would still play a role in the rate of energy transfer.
It does.
The power transmitted is the same (this follows from energy conservation and the requirement of steady state), but as the conductivity is different the temperature gradient is different.

It does.
The power transmitted is the same (this follows from energy conservation and the requirement of steady state), but as the conductivity is different the temperature gradient is different.
Yes, I understand the second part, but why would the power be the same through both? What about something being in "steady state" makes that happen?

mfb
Mentor
Imagine 100 W of heat transferred from one side to the center and 200 W transferred from the center to the other side. You now have a device which produces 100 W thermal power out of nowhere and violates energy conservation.

By definition....steady state means steady temperatures and therefore steady rate of flow of energy. Ie constant power Through the materials , assuming no power loss through the sides.