If the temperature of glass and water is decreased to 20.0 ∘C, how much water could be added to the glass?
Coefficient of linear expansion for Water: 210*10^-6
Coefficient of linear expansion for Water: 9*10^-6
I've tried everything and tried looking up how to do it as well, but no one has gotten the answer right. Please help!!!
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Verified answer
Linear exp. coef. for water, α = 210^-6 K⁻¹.. .. volume exp.coef. γ(w) = 3α = 630^-6 K⁻¹
Linear exp. coef. for glass, α = 9.0^-6 K⁻¹.. .. volume exp.coef. γ(g) = 3α = 27.0^-6 K⁻¹
From the volume expansion equation .. .. change in volume .. ∆V = Vi.γ.∆θ
Vi = 440 mL, ∆θ = -80°C
Net change in volume of water+glass, ∆V(net) = ∆V(w) + ∆V(g) .. (both shrink in volume)
∆V(net) = Vi.γ(w).∆θ + Vi.γ(g).∆θ
∆V(net) = Vi.∆θ { γ(w) + γ(g) } = 440 x -80 { 630^-6 + 27.0^-6 } = - 23.10 mL
Spare volume at 20°C .. .. ►∆V(net) = 23.10 mL