A one litre flask contains some mercury. It is found that at different temperature the volume of air inside the flask remains the same. What is the volume of the mercury in the flask? (alpha of glass is 9 xx 10 ^(-6)//^(@)C and Y _(R) of Hg is 1.8 xx 10 ^(-4) //^(@)C)

A one litre flask contains some mercury. It is found that at different

1.	A one litre flask contains some mercury. It is found that at different temperature the volume of air inside the flask remains the same. What is the volume of the mercury in the flask? (alpha of glass is 9 xx 10 ^(-6)//^(@)C and Y _(R) of Hg is 1.8 xx 10 ^(-4) //^(@)C)
Answer» Solution :Coefficient of volume expansion of the flask `(gamma) = 3 alpha = 3 xx 9 xx 10 ^(-6) = 27 xx 10&(-6) //^(@)C` Coefficient of volume expansion of `Hg = 1.8 xx 10 ^(-4) //^(@)C` Total volume of the flask (v) = 1 LITRE `= 1000 cm ^(3).` Let .x. be the volume of the mercury in the flask. If the expansion of teh mercury is same as the expansion of the flask then the space in the flask remains the same. Expansion of te flask for the rise of `t ^(@)C = v gamma t` Expansion of the mercury for the rise of `t ^(@)C = v gamma _(g) t therefore x gamma _(R )t = v gamma t` `implies x = (v gamma)/( gamma _(R)) = 100 xx (27 xx 10 ^(-6))/( 1.8 xx 10^(-4)) = 150 cm ^(3)`