Question

A garden flask with volume 200cm^3 is filled to the brim with mercury at 20°C.How much mercury overflows when the temperature of the system is raised to 100°C? The coefficient of linear expansion of the glass is 0.40×10^-5 K^-1 . Cubical expansion of mercury = 18×10^-5 K^-1.​

Answer 1

⊛ Solution ⊛

• $The \: coefficient \: of \: volume \: expansion \\ \: for \: the \: glass \: is \: \gamma glass \: = 3d \: glass \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1.2 \times 10 {}^{ - 5} k {}^{ - 1}$
• $The \: increase \: in \: volume \: of \: the \: \\ glass \: flask \: is \: ∆Vglass \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \gamma glass \:V0 \: ∆T$

$= (1.2 \times 10 {}^{ - 5} k {}^{ - 1})(200cm {}^{3} ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (100°C - 20°C)$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 0.19cm {}^{3}$

The increase in volume of the mercury is ∆Vmercury = γ mercury V0 ∆T

= ∆Vmercury = γ mercury V0 ∆T

$= (18 \times 10 {}^{ - 5} k {}^{ - 1})(200cm{}^{3}) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (100°C - 20 °C)$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2.9cm {}^{3}$

$∴ The \: volume \: of \: mercury \: that \: \\ overflows \: is \: \\ ∆Vmercury \: - ∆Vglass \: = 2.7cm {}^{3}.$

$@ANSWERER }$

Answer 2

Explanation:

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