Consider a plane composite slab made of different homogeneous layers arranged one…

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

Consider a plane composite slab made of

n

different homogeneous layers arranged one after another along the direction of heat flow. The

i

-th layer has thickness

L_i

and thermal conductivity

k_i

. All layers have the same cross-sectional area

A

. (i) Derive a general expression for the steady heat flow rate

\dfrac{Q}{t}

through the slab when the two outer faces are maintained at fixed temperatures

T_1

and

T_2

(

T_1 > T_2

). (ii) A brick wall

(k = 0.60\,\text{W}\,\text{m}^{-1}\,\text{K}^{-1})

of thickness

20\,\text{cm}

encloses a room of area

5\,\text{m}^2

. The indoor temperature is to be maintained at

20^{\circ}\,\text{C}

while the outside temperature is

40^{\circ}\,\text{C}

. Determine the minimum thickness of an insulation layer

(k = 0.04\,\text{W}\,\text{m}^{-1}\,\text{K}^{-1})

that must be added to the outside of the brick so that the rate of heat flow into the room is reduced by

60\,%

compared with the un-insulated brick wall.