A method for determining the thermal conductivity k and the specific heat cp of a material is illustrated in the sketch. Initially the two identical samples of diameter D= 60 mm and thickness L= 10 mm and the thin heater are at a uniform temperature of Ti= 23.00°C, while surrounded by an insulating powder. Suddenly the heater is energized to provide a uniform heat flux qo" on each of the sample interfaces, and the heat flux is maintained constant for a period of time, Δto. A short time after sudden heating is initiated, the temperature at this interface To is related to the heat flux as To(t)-Ti=2qo"(tπrhocpk)1/2. For a particular test run, the electrical heater dissipates 13.5 W for a period of Δto= 120 s, and the temperature at the interface is To(30 s)= 24.57 °C after 30 s of heating. A long time after the heater is deenergized, t≫Δ to, the samples reach the uniform temperature of [infinity] To([infinity])= 33.50 °C. The density of the sample materials determined by measurement of volume and mass, is rho= 6991 kg/m3. Required:
Determine the specific heat and thermal conductivity of the test material.