JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion JEE PYQ-Thermometry Calorimetry and Thermal Expansion

  • question_answer
    Two rods A and B of identical dimensions are at temperature \[30{}^\circ C\]. If A is heated upto \[180{}^\circ C\]and B upto \[T{}^\circ C\], then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is \[4:3\], then the value of T is- [JEE Main 11-Jan-2019 Evening]

    A)  \[200{}^\circ C\]           

    B)       \[270{}^\circ C\]

    C)  \[230{}^\circ C\]

    D)       \[250{}^\circ C\]

    Correct Answer: C

    Solution :

    [c] \[\Delta {{l}_{A}}=\Delta {{l}_{B}}\]
    \[{{l}_{OA}}{{\alpha }_{A}}{{(\Delta T)}_{A}}={{l}_{OB}}{{\alpha }_{B}}{{(\Delta T)}_{B}}\]
    \[\frac{\Delta T{{)}_{A}}}{{{(\Delta T)}_{B}}}=\frac{{{l}_{OB}}}{{{l}_{OA}}}\times \frac{{{\alpha }_{B}}}{{{\alpha }_{A}}}\]
    \[\frac{180-30}{T-30}=1\times \frac{3}{4}\]
    \[3T-90=600;T={{230}^{o}}C\]


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