A Partition Wall Has Two Layers A And B In Contact Each Made Of A Different Material. They Have The Same Thickness But The Thermal Conductivity Of Layer A Is Twice That Of B. If The Steady State Temperature Difference Across Layer B Is 60K, Then The Corresponding Temperature Difference Across Layer A Is____
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Consider two walls 'A' and 'B' of thickness 't' each, and thermal conductivity of '2K' and 'K' respectively.
The temperatures at the left of A = T
a
The temperatures at the right of B = T
b
The temperature at the junction = T
Heat flow is a constant in steady state:
Q
˙
=KA
dx
dT
=constant
Equating heat flow for both walls we get:
2KA
t−0
T−T
a
=KA
2t−t
T
b
−T
Which simplifies to: 3T=T
b
+2T
a
Also given that the temperature difference between the walls is 36
∘
C
T
b
−T
a
=36
Combining the two equation in T,T
a
,T
b
and eliminating T
b
We get T−T
a
=12
∘
C
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