The thermal conductivity of a solid whose density and specific heat are known can be determined from the relation k = α/ρc_p after evaluating the thermal diffusivity a. Consider a 2-cm-diameter cylindrical rod made of a sample material whose density and specific heat are 3700 kg/m³ and 920 J/kg · K, respectively. The sample is initially at a uniform temperature of 25°C. In order to measure the temperatures of the sample at its surface and its center, a thermocouple is inserted to the center of the sample along the centerline, and another thermocouple is welded into a small hole drilled on the surface. The sample is dropped into boiling water at 100°C. After 3 min, the surface and the center temperatures are recorded to be 93°C and 75°C, respectively. Determine the thermal diffusivity and the thermal conductivity of the material.

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T surface Rod Boiling water 100°C Thermocouples Tcenter