A copper sphere is to be quenched in an oil bath whose temperature is 50°C. The sphere's radius is 30 mm, and the convection coefficient is h = 300 W/(m2.°C). Assume the sphere and the oil properties are constant. These properties are given in the following table. The sphere's initial temperature is 400°C.

Assume that the volume of the oil bath is large enough so that its temperature does not change when the sphere is immersed in the bath. Obtain the dynamic model of the sphere's temperature T. How long will it take for T to reach 130°C?

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Property Density p (kg/m') Specific heat cp J(kg . °C) 385 400 Thermal conductivity k Sphere Oil 8900 7900 400