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The diagram is for three materials with different thermal conductivities. I think number 1 is the material with higher thermal conductivity because it transfers the heat faster so it gets to the steady temperature sooner than the other two. Am I right? If not or if my reasoning isn't correct, I appreciate your help.

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$\dot{Q} = k A \frac{\Delta T}{l}$

$l$ thickness

$A$ surface area

From this follows that besides other factors the rate of heatflow is proportional to the thermal conductivity $k$.

$\dot{Q} \propto k$

Therefore a high thermal conductivity allows for a fast heat transfer, hence your interpretation that a fast change in temperature correlates with a high thermal conductivity is right.

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