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Question
The volume of glass vessel is 1000cc at 20∘C. What volume of mercury should be poured into it at this temperature so that the volume of the remaining space does not change with temperature? Coefficient of cubical expansion of mercury and glass are 1.8×10−4/∘Cand9.0×10−5/∘C respectively.
The volume of glass vessel is 1000cc at 20∘C. What volume of mercury should be poured into it at this temperature so that the volume of the remaining space does not change with temperature? Coefficient of cubical expansion of mercury and glass are 1.8×10−4/∘Cand9.0×10−5/∘C respectively.
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Solution
The correct option is B 500cc.
Let volume of mercury added at 20oC be Vm. So at 20oC, volume of remaining space is 1000−Vm −(1) Now due to thermal expansion the volume changes as: Volume of glass vessel V2g=1000(1+9×10−5θ) and, Volume of mercury V2m=Vm(1+18×10−5θ) where θ is the change in temperature. Now the volume of remaining space is V2g−V2m=1000−Vm+9×10−2×θ−18Vm×10−5×θ −(2) Equating (1) and (2)
we get Vm=9×10−2/18×10−5=50cc
Let volume of mercury added at 20oC be Vm. So at 20oC, volume of remaining space is 1000−Vm −(1) Now due to thermal expansion the volume changes as: Volume of glass vessel V2g=1000(1+9×10−5θ) and, Volume of mercury V2m=Vm(1+18×10−5θ) where θ is the change in temperature. Now the volume of remaining space is V2g−V2m=1000−Vm+9×10−2×θ−18Vm×10−5×θ −(2)
Equating (1) and (2)
we get Vm=9×10−2/18×10−5=50cc
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