Final answer:
To match the thermal conduction rate of a silver saucepan with a less expensive material, compare their thermal conductivities and adjust the pan's thickness to compensate for any differences in material properties, ensuring the new pan is not more than 50% larger in surface area.
Step-by-step explanation:
To design a saucepan with the same rate of thermal conduction as one made from silver, without using silver, you have to consider different properties of materials such as thermal conductivity, thickness, and size. Assuming that the pan's surface area cannot exceed 50% more than the silver pan, we must look into other materials that have a lower thermal conductivity than silver and adjust the thickness accordingly to achieve the desired thermal conduction rate.
You can use to find the thermal conductivity values for different materials. For instance, if copper has a thermal conductivity that is less than that of silver, the copper pan's thickness may need to be decreased to allow for a similar rate of conduction. The design should ensure that the new material, while being cost-effective, still conducts heat efficiently to serve the purpose of a saucepan efficiently.