Question

Wearing layers of clothing in cold weather is often recommended because dead-air spaces between the layers keep the body warm by reducing the heat loss from the body. Compare the rate of heat loss for a single, 13 mm thick layer of wool to three 3 mm thick layers separated by 2 mm air gaps. Since the air gaps are so small, treat the air as stationary (i.e., assume heat is being conducted through the air gaps). Use kwool = 0.07 W/m-K and kair = 0.02 W/m-K.

Answer 1

Three 3 mm thick layers separated by 2 mm air gaps will provide more warmth

Step-by-step explanation:

Given data :

K wool = 0.07 W/m-k

Kair = 0.02 W/m-k

i) calculating the rate of heat loss for a 13 mm thick layer of wool:

thickness = 13 mm = 0.013

Q1 = 7/13 ΔT w/m^2

ii) determining the rate of heat loss for three 3 mm thick layer of wool with 2 mm air gaps

Q2 = 23/70 ΔT w/m^2

When comparing the rate of heat loss for a single 13 mm thick layer of wool to three 3 mm thick layers separated by 2 mm air gaps it can be observed that three 3 mm thick layers separated by 2 mm air gaps will provide more warmth : Q1 > Q2