Properties Of Solids And Liquids Question 394
Question: The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively, are$ {{T} _{2}} $ and $ T _{1} $
$ ({{T} _{2}}>T _{1}) $ . The rate of heat transfer through the slab, in a steady state is $ ( \frac{A( {{T} _{2}}>T _{1} )K}{x} )f $ , with f equal to
Options:
A) $ \frac{2}{3} $
B) $ \frac{1}{2} $
C) 1
D) $ \frac{1}{3} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] the thermal resistance is given by $ \frac{x}{KA}+\frac{4x}{2KA}=\frac{x}{KA}+\frac{2x}{KA}=\frac{3x}{KA} $
$ \therefore \frac{dQ}{dt}=\frac{\Delta T}{\frac{3x}{KA}}=\frac{( T _{2}-T _{1} )KA}{3x} $
$ =\frac{1}{3}{ \frac{A( T _{2}-T _{1} )K}{x} }\therefore f=\frac{1}{3} $
