Consider two walls, A and B, with the same surface areas and the same temperature drops across their thicknesses. The ratio of their thermal

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

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Vân Khánh 1 year 2021-08-23T20:35:12+00:00 1 Answers 385 views 0

Answers ( )

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    2021-08-23T20:36:21+00:00

    Answer:

    (c) 2

    Explanation:

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

    [tex]q = -KA\frac{\Delta T}{L}[/tex]

    where,

    q = heat transfer rate

    K = thermal conductivity

    A = Area

    ΔT = change in temperature

    L = thickness

    For wall A:

    [tex]q_A = -K_AA\frac{\Delta T}{L_A}[/tex]

    For wall B:

    [tex]q_B = -K_BA\frac{\Delta T}{L_B}[/tex]

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

    [tex]\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}}[/tex]

    using values given in the question:

    [tex]\frac{q_A}{q_B} = \frac{4}{2}\\\\\frac{q_A}{q_B} = 2[/tex]

    Therefore, the correct answer is:

    (c) 2

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