Final answer:
The heat transferred by conduction into the sole of a firewalker's foot is approximately 125 J.
Step-by-step explanation:
To calculate the heat transferred by conduction into the sole of the firewalker's foot, we can use the formula Q = k * A * (ΔT / d) * t, where Q is the heat transfer, k is the thermal conductivity, A is the area of contact, ΔT is the temperature difference, d is the thickness of the callus, and t is the time in contact. First, convert the thickness of the callus from millimeters to meters: d = 3.00 mm / 1000 = 0.003 m. Next, use the formula to calculate the heat transfer:
Q = (k * A * ΔT * t) / d
Plugging in the given values:
Q = (k * 0.025 m² * (700 °C - 0 °C) * 1 s) / 0.003 m
Using the average thermal conductivity of wood, which is approximately 0.1 W/(m·K), we can calculate the heat transfer:
Q = (0.1 W/(m·K) * 0.025 m² * (700 °C - 0 °C) * 1 s) / 0.003 m
Simplifying the equation gives:
Q ≈ 125 J
Therefore, the correct answer is option a) 125 J.