Chapter 5, Problem 5.90P

A procedure for determining the thermal conductivity of a solid material involves embedding a thermocouple in a thick slab of the solid and measuring the response to a prescribed change in temperature at one surface. Consider an arrangement for which the thermocouple is embedded from a surface that is suddenlybrought to a temperature of $100°\text{C}$  by exposure to boiling water. If the initial temperature of the slab was $30°\text{C}$  and the thermocouple measures a temperature of $65°\text{C,}$ 2 min after the surface is brought to $100°\text{C,}$ what is its thermal conductivity? The density and specific heat of the solid are known to be and $700\text{J/kg}\cdot \text{K}\text{.}$