4. (10 points) Consider the diffusion in a coupled alloy is governed by the transformed second Fick's law as C_{x}=\left(\frac{C_{1}+C_{2}}{2}\right)-\left(\frac{C_{1}-C_{2}}{2}\right) \operatorname{erf}\left(\frac{x}{2 \sqrt{D t}}\right) C, is the concentration of metal in

one alloy, while C, is the concentration of metal in the coupled alloy. Now for case hardening, a diffusion couple composed of two silver-gold alloys is formed;these alloys have compositions of 98 wt% Ag-2 wt% Au and 95 wt% Ag-5 wt% Au.Determine the time this diffusion couple must be heated at 750°C (1023 K) in order for the composition to be 2.5 wt% Au at the 50 um position into the 2 wt% Au side of the diffusion couple. Assume the per-exponential and activation energy values for Au diffusion in Ag are8.5x10-5 m²/s and 202100 J/mol, respectively.

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