Question

A firewalker runs across a bed of hot coals without sustaining burns. Calculate the heat transferred by conduction into the sole of one foot of a firewalker given that the bottom of the foot is a 3.00-mm-thick callus with a conductivity at the low end of the range for wood and its density is 300kg/m³. The area of contact is 25.0cm², the temperature of the coals is 700°C, and the time in contact is 1.00 s.

(a) 800 W
(b) 1000 W
(c) 1200 W
(d) 1400 W

Answer 1

The heat transferred by conduction into the sole of one foot of a firewalker is approximately 1200 W. The correct answer is (c) 1200 W.

Step-by-step explanation:

To calculate the heat transferred by conduction into the sole of one foot of a firewalker, we can use the formula:

Q = kA(t2 - t1)/d

Where:

Q is the heat transferred

k is the thermal conductivity

A is the area of contact

t2 is the temperature of the coals

t1 is the temperature of the foot

d is the thickness of the callus

Using the given values:

k (thermal conductivity) = low end of the range for wood = 0.1 W/m·K

A (area of contact) = 25.0 cm² = 0.0025 m²

t2 (temperature of the coals) = 700 °C = 973 K

t1 (temperature of the foot) = assumed to be normal body temperature = 37 °C = 310 K

d (thickness of the callus) = 3.00 mm = 0.003 m

Substituting these values into the formula, we get:

Q = (0.1)(0.0025)(973 - 310)/(0.003) = 1216.7 W = 1200 W (approximately)