NEET Sample Paper NEET Sample Test Paper-1

  • question_answer Two rods having thermal conductivity in the ratio of \[5:3\] having same length area equal cross-sectional area are join by face to face. If the temperature of the free end of the first rod is \[{{100}^{o}}C\] and the temperature of free end of the second rod is \[{{20}^{o}}C\]. Then temperature of junction will be:

    A)  \[{{85}^{o}}C\]                 

    B)  \[{{90}^{o}}C\]

    C)  \[{{50}^{o}}C\]              

    D)  \[{{70}^{o}}C\]

    Correct Answer: D

    Solution :

    Thermal conductivity of first rod \[{{K}_{1}}=5\alpha \] and thermal conductivity of second rod \[{{K}_{2}}=3\,\alpha \] Temperature of the first rod \[{{T}_{1}}={{100}^{o}}C\] and Temperature of second rod \[{{T}_{2}}={{20}^{o}}C\]. In the steady state, the rate of heat transfer in  both the conductors will be same \[\therefore \]  \[\frac{{{K}_{1}}A({{T}_{1}}-T)}{d}=\frac{{{K}_{2}}A(T-{{T}_{1}})}{d}\] Where T is the temperature of the junction) \[\Rightarrow \]               \[{{K}_{1}}({{T}_{1}}-T)={{K}_{2}}(T-{{T}_{2}})\] \[\Rightarrow \]               \[5\alpha (100-T)=3\alpha (T-20)\] \[\Rightarrow \]               \[5(100-T)=3\,(T-20)\] \[\Rightarrow \]               \[500-5T=3T-60\] \[\Rightarrow \]               \[8T=560\] \[\Rightarrow \]               \[T={{70}^{o}}C\]

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