question_answer

The coefficient of linear expansion of glass is \[{{\alpha }_{g}}\] per \[{}^\circ C\]and the cubical expansion of mercury is y\[{{\gamma }_{m}}\] per \[{}^\circ C\]. The volume of the bulb of a mercury thermometer at \[0{}^\circ C\]is \[{{V}_{0}}\] and cross section of the capillary is \[{{\operatorname{A}}_{0}}\]. What is the length of mercury column in capillary at \[T{}^\circ C\], if the mercury just fills the bulb at \[0{}^\circ C\]?

A) \[\frac{{{\operatorname{V}}_{0}}T\left( {{\gamma }_{\operatorname{m}}}+3{{\alpha }_{\operatorname{g}}} \right)}{{{\operatorname{A}}_{0}}\left( 1+2{{\alpha }_{\operatorname{g}}}T \right)}\]

B)  \[\frac{{{\operatorname{V}}_{0}}T\left( {{\gamma }_{\operatorname{m}}}-3{{\alpha }_{\operatorname{g}}} \right)}{{{\operatorname{A}}_{0}}\left( 1+2{{\alpha }_{\operatorname{g}}}T \right)}\]

C) \[\frac{{{\operatorname{V}}_{0}}T\left( {{\gamma }_{\operatorname{m}}}+2{{\alpha }_{\operatorname{g}}} \right)}{{{\operatorname{A}}_{0}}\left( 1+3{{\alpha }_{\operatorname{g}}}T \right)}\]

D) \[\frac{{{\operatorname{V}}_{0}}T\left( {{\gamma }_{\operatorname{m}}}-2{{\alpha }_{\operatorname{g}}} \right)}{{{\operatorname{A}}_{0}}\left( 1+3{{\alpha }_{\operatorname{g}}}T \right)}\]