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

(c) 2

Step-by-step explanation:

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

`q = -KA(\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(\Delta T)/(L_A)`

For wall B:

`q_B = -K_BA(\Delta T)/(L_B)`

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

`(q_A)/(q_B) = ((K_A)/(L_A) )/((K_B)/(L_B))\\\\ (q_A)/(q_B) =((K_A)/(K_B) )/((L_A)/(L_B))`

using values given in the question:

`(q_A)/(q_B) = (4)/(2)\\\\(q_A)/(q_B) = 2`

Therefore, the correct answer is:

(c) 2