Transmission Of Heat Question 54
Question: If two metallic plates of equal thicknesses and thermal conductivities $ K _{1} $ and $ K _{2} $ are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be
[MP PMT 1991]
Options:
A) $ \frac{K _{1}K _{2}}{K _{1}+K _{2}} $
B) $ \frac{2K _{1}K _{2}}{K _{1}+K _{2}} $
C) $ \frac{{{(K _{1}^{2}+K _{2}^{2})}^{3/2}}}{K _{1}K _{2}} $
D) $ \frac{{{(K _{1}^{2}+K _{2}^{2})}^{3/2}}}{2K _{1}K _{2}} $
Show Answer
Answer:
Correct Answer: B
Solution:
In series $ R _{eq}=R _{1}+R _{2} $
Therefore $ \frac{2l}{K _{eq}A}=\frac{l}{K _{1}A}+\frac{l}{K _{2}A} $
Therefore $ \frac{2}{K _{eq}}=\frac{1}{K _{1}}+\frac{1}{K _{2}} $
Therefore $ K _{eq}=\frac{2K _{1}K _{2}}{K _{1}+K _{2}} $
BETA
