JEE Main & Advanced Physics Transmission of Heat Question Bank Topic Test - Transmission of Heat (3-5-21)

  • question_answer
    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

    A) \[{{50}^{o}}C\]

    B) \[\frac{100}{3}{{\ }^{o}}C\]

    C) \[{{60}^{o}}C\]

    D) \[\frac{200}{3}{{\ }^{o}}C\]

    Correct Answer: C

    Solution :

    Temperature of interface             \[\theta =\frac{{{K}_{1}}{{\theta }_{1}}{{l}_{2}}+{{K}_{2}}{{\theta }_{2}}{{l}_{1}}}{{{K}_{1}}{{l}_{2}}+{{K}_{2}}{{l}_{1}}}\]\[=\frac{K\times 0\times 2+3K\times 100\times 1}{K\times 2+3K\times 1}\]               \[=\frac{300K}{5K}\]\[=60{}^\circ C\]

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