Properties Of Solids And Liquids Question 537
Question: 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 $ \alpha $ for steel is $ 12\times {{10}^{-6}}/{}^\circ C, $ then that of glass is
Options:
A) $ 9\times {{10}^{-6}}/{}^\circ C $
B) $ 6\times {{10}^{-6}}/{}^\circ C $
C) $ 36\times {{10}^{-6}}/{}^\circ C $
D) $ 27\times {{10}^{-6}}/{}^\circ C $
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Answer:
Correct Answer: A
Solution:
$ {\gamma _{real}}={\gamma _{app.}}+{\gamma _{vessel}} $ So $ {{( {{\gamma} _{\text{app}\text{.}}}\text{+ }{{\gamma} _{\text{vessel}}} )} _{\text{glass}}}\text{=}{{( {{\gamma} _{\text{app}\text{.}}}\text{+ }{{\gamma} _{\text{vessel}}} )} _{\text{steel}}} $
$ \Rightarrow \text{153 }\times\text{ 1}{{\text{0}}^{\text{-6}}}\text{+}{{( {{\gamma} _{\text{vessel}}} )} _{\text{glass}}}\text{=}{{( \text{144 }\times\text{ 1}{{\text{0}}^{\text{-6}}}\text{+}{{\gamma} _{\text{vessel}}} )} _{\text{steel}}} $
$ Further,{{( {\gamma _{vessel}} )} _{steel}}=3\alpha =3\times ( 12\times {{10}^{-6}} )=36\times {{10}^{-6}}/{}^\circ C $
$ \Rightarrow 153\times {{10}^{-6}}+{{( {\gamma _{veseel}} )} _{glass}}={{( 144\times {{10}^{-6}}+{\gamma _{vessel}} )} _{steel}} $
$ \Rightarrow {{( {\gamma _{vessel}} )} _{glass}}=3\alpha =27\times {{10}^{-6}}+36\times {{10}^{-6}} $
$ \Rightarrow \alpha =9\times {{10}^{-6}}/{}^\circ C $
