A glass flask of volume $200 c m^{3}$ is just filled with mercury at $20 C$ . The amount of mercury that will overflow when the temperature of the system is raised to $100 C$ is: $γ_{g l a s s} = 1.2 \times 10^{- 5} / C^{\circ}, γ_{m e r c u r y} = 1.8 \times 10^{- 4} / C^{\circ}$

2.15 c m^{3}

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2.69 c m^{3}

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2.52 c m^{3}

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2.25 c m^{3}

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Solution

The correct option is C $2.69 c m^{3}$
$\begin{matrix} γ_{g l a s s} = \frac{Δ V}{V} = 1.2 \times 10^{- 5} Δ V_{g l a s s} = β_{g l a s s} V_{0} Δ T = (1.2 \times 10^{- 5}) (200) (100 - 20) = 0.19 c m^{3} Δ V_{m e r c u r y} = β_{m e r c u r y} V_{0} Δ T = (1.8 \times 10^{- 5}) (200) (100 - 20) = 2.9 c m^{3} Δ V_{m e r c u r y} - Δ V_{g l a s s} = 2.9 - 0.19 = 2.7 \end{matrix}$
Hence option (B) is correct.

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Similar questions

Q. A glass flask of volume

200 {cm}^{3}

is just filled with mercury at

20^{\circ} C

. The amount of mercury that will overflow when the temperature of the system is raised to

100^{\circ} C

(γ_{glass} = 1.2 \times 10^{- 5}^{\circ} C^{- 1}, γ_{mercury} = 1.8 \times 10^{- 4}^{\circ} C^{- 1})

Q. A glass vessel of volume

200 {cm}^{3}

is filled with mercury and is heated from

25^{o} C

75^{o} C

. What volume of mercury will overflow? Coefficient of linear expansion of glass =

1.8 \times 10^{- 6} /^{o} C

and coefficient of volumetric expansion of mercury is

1.8 \times 10^{- 4} /^{o} C

A glass vessel measures exactly 10 cm $\times$ 10 cm $\times$ 10 cm at $0^{\circ} C$ . It is filled completely with mercury at this temperature. When the temperature is raised to $10^{\circ} C$ , $1.6 c m^{3}$ of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass $= 6.5 \times 10^{- 6}^{\circ} C^{- 1}$ .

A glass bulb of volume 250cc is filled with mercury at 20 $^{0}$ C and the temperature is raised to $100^{0} C$ . If the coefficient of linear expansion of glass is $9 \times 10^{- 6 / 0} C$ Coefficient of absolute expansion of mercury is $18 \times 10^{- 4 / 0} C$ . The volume of mercury that overflows is

Q. A glass vessel of volume

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is filled with mercury and is heated from

25^{\circ} C t o 75^{\circ} C

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and coefficient of volume expansion of mercury is

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A glass flask of volume 200cm3 is just filled with mercury at 20C. The amount of mercury that will overflow when the temperature of the system is raised to 100C is: γglass=1.2×10−5/C∘,γmercury=1.8×10−4/C∘

The correct option is C 2.69cm3γglass=ΔVV=1.2×10−5ΔVglass=βglassV0ΔT=(1.2×10−5)(200)(100−20)=0.19cm3ΔVmercury=βmercuryV0ΔT=(1.8×10−5)(200)(100−20)=2.9cm3ΔVmercury−ΔVglass=2.9−0.19=2.7Hence option (B) is correct.

A glass flask of volume $200 c m^{3}$ is just filled with mercury at $20 C$ . The amount of mercury that will overflow when the temperature of the system is raised to $100 C$ is: $γ_{g l a s s} = 1.2 \times 10^{- 5} / C^{\circ}, γ_{m e r c u r y} = 1.8 \times 10^{- 4} / C^{\circ}$