How much glycerin must be placed inside a glass vessel of capacity 250 cc, so that volume of the space unoccupied by glycerin always remains constant?
Answers
Volume of glycerin = Volume of Vessel * volume coefficient of expansion of glass / volume coefficient of expansion of glycerin
Explanation:
Volume of glass = V = 250 cc
Volume of glycerin = v cc
V - v = space unoccupied
α = volume coefficient of expansion of glass
β = volume coefficient of expansion of glycerin
ΔT = Change in temperature
Vₙ = V( 1 + αΔT)
vₙ = v( 1 + βΔT)
Vₙ - vₙ = space unoccupied
space unoccupied remains constant
Vₙ - vₙ = V - v
=> V( 1 + αΔT) - v( 1 + βΔT) = V - v
=> V + VαΔT - v - vβΔT = V - v
=> vβΔT = VαΔT
=> vβ = Vα
=> v = Vα/β
=> v = 250α/β
Volume of glycerin = Volume of Vessel * volume coefficient of expansion of glass / volume coefficient of expansion of glycerin
if Values are given then substitute .
Assuming :
volume coefficient of expansion of glycerin = 0.000597 per °C
volume expansion of glass =3×0.000009=0.000027 per °C
v = 250α/β = 250 * 0.000027 / 0.000597
=> v = 11.3 cc
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Volume of glycerin = Volume of Vessel * volume coefficient of expansion of glass / volume coefficient of expansion of glycerin
Explanation:
Volume of glass = V = 250 cc
Volume of glycerin = v cc
V - v = space unoccupied
α = volume coefficient of expansion of glass
β = volume coefficient of expansion of glycerin
ΔT = Change in temperature
Vₙ = V( 1 + αΔT)
vₙ = v( 1 + βΔT)
Vₙ - vₙ = space unoccupied
space unoccupied remains constant
Vₙ - vₙ = V - v
=> V( 1 + αΔT) - v( 1 + βΔT) = V - v
=> V + VαΔT - v - vβΔT = V - v
=> vβΔT = VαΔT
=> vβ = Vα
=> v = Vα/β
=> v = 250α/β
Volume of glycerin = Volume of Vessel * volume coefficient of expansion of glass / volume coefficient of expansion of glycerin
if Values are given then substitute .
Assuming :
volume coefficient of expansion of glycerin = 0.000597 per °C
volume expansion of glass =3×0.000009=0.000027 per °C
v = 250α/β = 250 * 0.000027 / 0.000597
v = 250α/β = 250 * 0.000027 / 0.000597= 250α/β = 250 * 0.000027 / 0.000597=> v = 11.3 cc
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