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JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Question Bank Self Evaluation Test - Thermal Properties of Matter

  • question_answer
    The coefficient of apparent expansion of mercury in a glass vessel is \[153\times {{10}^{-6}}/{}^\circ C\] and in a steel vessel is \[144\times {{10}^{-6}}/{}^\circ C\]. If a for steel is \[12\times {{10}^{-6}}/{}^\circ C\], then that of glass is

    A) \[\]

    B) \[6\times {{10}^{-6}}/{}^\circ C\]

    C) (c)\[36\times {{10}^{-6}}/{}^\circ C\]

    D) \[27\times {{10}^{-6}}/{}^\circ C\]

    Correct Answer: A

    Solution :

    [a]  \[{{\gamma }_{real}}={{\gamma }_{app.}}+{{\gamma }_{vessel}}\] So \[{{\left( {{\gamma }_{\operatorname{app}.}}+{{\gamma }_{vessel}} \right)}_{glass}}={{\left( {{\gamma }_{app }}+{{\gamma }_{vessel}} \right)}_{steel}}\] \[\Rightarrow 153\times {{10}^{-6}}+{{\left( {{\gamma }_{vessel}} \right)}_{glass}}\] \[=144\times 1{{0}^{-6}}+{{\left( {{\gamma }_{vessel}} \right)}_{steel}}\] \[\operatorname{Further}{{({{\gamma }_{vessel}})}_{steel}}=3\alpha =3\times  (12\times 1{{0}^{-6}})\] \[=36\times {{10}^{-6}}{{/}^{o}}C\] \[\Rightarrow 153\times 1{{0}^{-6}}+{{\left( {{\gamma }_{vessel}} \right)}_{glass}}\] \[=144\times 1{{0}^{-6}}+36\times l{{0}^{-6}}\] \[{{\left( {{\gamma }_{vessel}} \right)}_{gIass}}=3\alpha =27\times 10{{/}^{o}}C\] \[\Rightarrow  a=9\times {{10}^{-6}}/{}^\circ C\]


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