Problem — Insulator efficiency

Problem

Four materials have the same thickness $d = 5$ cm but different thermal conductivity $k$ [in W/(m$\cdot$K)]: (A) glass wool $k = 0{,}04$; (B) expanded polystyrene $k = 0{,}035$; (C) cork $k = 0{,}045$; (D) still air $k = 0{,}025$. Rank the materials from best to worst insulator.

Solution

For the same thickness and surface area, the heat flow through a wall is: $\dot Q = \frac{k \, A \, \Delta T}{d}$

So $\dot Q$ is directly proportional to the conductivity $k$: the best insulator is the one that lets through the least heat, i.e. the one with the lowest $k$.

Ranking the values from smallest to largest: $k_D = 0{,}025 < k_B = 0{,}035 < k_A = 0{,}04 < k_C = 0{,}045$

$\ev{D < B < A < C \quad (\text{best} \to \text{worst})}$

Still air is the best insulator (it is precisely the trapped air that makes all the other porous materials insulating), while cork is the worst of the four.

Collegamenti

Argomenti: Termologia Concetti: Trasmissione del calore