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Question
A glass flask of volume one litre is filled completely with mercury at 0oC. The flask is now heated to 100oC. Coefficient of volume expansion of mercury is 1.82×10−4/oC and coefficient of linear expansion of glass is 0.1×10−4/oC. During this process, amount of mercury which overflows is :
A glass flask of volume one litre is filled completely with mercury at 0oC. The flask is now heated to 100oC. Coefficient of volume expansion of mercury is 1.82×10−4/oC and coefficient of linear expansion of glass is 0.1×10−4/oC. During this process, amount of mercury which overflows is :
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Solution
The correct option is A 15.2 cc
Since both mercury and glass will expand on heating but mercury will expand more than glass and hence, some mercury will spill out. Coefficient of volume expansion of glass will be γ=3α=0.3X10−4/0C.
Using ,ΔV=γ×V×ΔT
Mercury expansion will be (1.82X10−4)(100)(1000) cc=18.2 cc and vessel expansion will be (0.3X10−4)(100)(1000) cc=3 cc
Hence, volume of mercury spilled will be 18.2 cc−3 cc=15.2 cc
Since both mercury and glass will expand on heating but mercury will expand more than glass and hence, some mercury will spill out. Coefficient of volume expansion of glass will be γ=3α=0.3X10−4/0C.
Using ,ΔV=γ×V×ΔT
Mercury expansion will be (1.82X10−4)(100)(1000) cc=18.2 cc and vessel expansion will be (0.3X10−4)(100)(1000) cc=3 cc
Hence, volume of mercury spilled will be 18.2 cc−3 cc=15.2 cc
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