Question

Consider two walls, A and B, with the same surface areas and the same temperature drops across their thicknesses. The ratio of their thermal conductivities is kA/kB=4 and the ratio of the wall thickness is LA/LB=2. The ratio of heat transfer rates through the walls qA/qB is:
(a) 0.5

(b) 1

(c) 2

(d) 4

(e) 8

(f) None of them

Answer 1

Answer:

(c) 2

Explanation:

Heat transfer across the walls due to conduction is given by:

$q = -KA\frac{\Delta T}{L}$

where,

q = heat transfer rate

K = thermal conductivity

A = Area

ΔT = change in temperature

L = thickness

For wall A:

$q_A = -K_AA\frac{\Delta T}{L_A}$

For wall B:

$q_B = -K_BA\frac{\Delta T}{L_B}$

Because the change of temperature and area of walls are the same. Dividing both terms:

$\frac{q_A}{q_B} = \frac{\frac{K_A}{L_A} }{\frac{K_B}{L_B}}\\\\ \frac{q_A}{q_B} =\frac{\frac{K_A}{K_B} }{\frac{L_A}{L_B}}$

using values given in the question:

$\frac{q_A}{q_B} = \frac{4}{2}\\\\\frac{q_A}{q_B} = 2$

Therefore, the correct answer is:

(c) 2