Transmission Of Heat Question 306
Question: Two bars of thermal conductivities K and 3K and lengths $ 1cm $ and $ 2cm $ respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is $ 0^{o}C $ and $ K^{2}/l $ respectively (see figure), then the temperature $ \varphi $ of the interface is
Options:
A) $ 50^{o}C $
B) $ \frac{100}{3}{{\ }^{o}}C $
C) $ 60^{o}C $
D) $ \frac{200}{3}{{\ }^{o}}C $
Show Answer
Answer:
Correct Answer: C
Solution:
Temperature of interface $ \theta =\frac{K _{1}{\theta _{1}}l _{2}+K _{2}{\theta _{2}}l _{1}}{K _{1}l _{2}+K _{2}l _{1}} $
$ =\frac{K\times 0\times 2+3K\times 100\times 1}{K\times 2+3K\times 1} $
$ =\frac{300K}{5K} $
$ =60{}^\circ C $
BETA
