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A glass flask whose volume is 1000.29 cm3 at 0.0∘C is completely filled with mercury at...

A glass flask whose volume is 1000.29 cm3 at 0.0∘C is completely filled with mercury at this temperature. When flask and mercury are warmed to 55.4 ∘C, 8.98 cm3 of mercury overflow.

Compute the coefficient of volume expansion of the glass. (The coefficient of volume expansion of the mercury is 18×10−5K−1.)

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Answer #1

Initial volume of the mercury = Initial volume of glass flask = Vo = 1000.29 cm^3

Volume of mercury overflows after heating = 8.98 cm^3

Now, the total volume of mercury after heating it to 55.4 deg C,

Vt = Vo[1+γ∆t]

=>Vt = 1000.29*[1+1.80 x 10^-4 x (55.4 - 0)]

=>Vt = 1000.29*[1 + 0.009972]

= 1010.3 cm^3

=>Thus Vt of glass = 1010.3 - 8.98 = 1001.32 cm^3

Again for glass,

Vt = Vo[1+γ∆t]

=> 1001.32 = 1000.29 *[1+γ x (55.4 - 0)]

=> 1+γ x 55.4 = 1001.32 / 1000.29 = 1.0010297

=> γ x 55.4 = 0.0010297

=> γ = 0.0010297 / 55.4 = 1.86 x 10^-5 / K

Therefore, coefficient of volume expansion of glass, γ = 1.86 x 10^-5 /K (Answer)

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