The coefficient of thermal conductivities of the metals are K and \[2K\]respectively. If the furnace temperature at one end is \[{{300}^{o}}C\]and ice box temperature at the other end is \[{{0}^{o}}C,\] then the junction temperature is
A) \[{{100}^{o}}C\]
B) \[{{125}^{o}}C\]
C) \[{{150}^{o}}C\]
D) \[{{200}^{o}}C\]
Correct Answer: A
Solution :
Temperature of interface \[\theta =\frac{{{k}_{1}}{{\theta }_{1}}{{l}_{2}}+{{k}_{2}}{{\theta }_{2}}{{l}_{1}}}{{{k}_{1}}{{l}_{2}}+{{k}_{2}}{{l}_{1}}}\] \[=\frac{2k\times 0\times l+k\times 300\times l}{kl+2kl}={{100}^{o}}C\]
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