A Bakelite beaker has volume capacity of $$500$$ cc at $$30$$ºC. When it is partially filled with Vm volume (at$$ $$30$$º$$C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varies. If γ$$beaker=6$$×$$10$$−$$6$$ºC−$$1$$ and γ$$mercury=1.5$$×$$10$$−$$4$$ºC−$$1$$, where γ is the coefficient of volume expansion, then Vm (in$$ $$cc) is close to $$________$$.

Question

A Bakelite beaker has volume capacity of $$500$$ cc at $$30$$ºC. When it is partially filled with  Vm volume (at$$ $$30$$º$$C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varies. If γ$$beaker=6$$×$$10$$−$$6$$ºC−$$1$$ and  γ$$mercury=1.5$$×$$10$$−$$4$$ºC−$$1$$, where γ is the coefficient of volume expansion, then Vm  (in$$ $$cc) is close to $$________$$.

Infinity Learn · Accepted Answer

Δ$$Vbeaker=$$ΔVmercury⇒γbeaker Vbeaker $$=$$γmercuryVmercury⇒$$6$$×$$10-6500=1.5$$×$$10-4Vm$$⇒$$Vm=20$$ cc

Thermal expansion

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$\begin{array}{l} Δ V_{beaker} = Δ V_{m e r c u r y} \\ \Rightarrow γ_{beaker} V_{beaker} = γ_{m e r c u r y} V_{m e r c u r y} \\ \Rightarrow (6 \times 10^{- 6}) 500 = (1.5 \times 10^{- 4}) V_{m} \\ \Rightarrow V_{m} = 20 c c \end{array}$

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Thermal expansion

Unlock the full solution & master the concept.

ΔVbeaker=ΔVmercury⇒γbeaker Vbeaker =γmercuryVmercury⇒6×10-6500=1.5×10-4Vm⇒Vm=20 cc

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$\begin{array}{l} Δ V_{beaker} = Δ V_{m e r c u r y} \\ \Rightarrow γ_{beaker} V_{beaker} = γ_{m e r c u r y} V_{m e r c u r y} \\ \Rightarrow (6 \times 10^{- 6}) 500 = (1.5 \times 10^{- 4}) V_{m} \\ \Rightarrow V_{m} = 20 c c \end{array}$