Respuesta :
Answer:
14.64% of the volume of the glass, more water can be added
Explanation:
given:
Initial temperature, = 100°C = 373K
Final temperature = 20°C = 293K
Coefficient of volume expansion for glass, = 2.7 x 10⁻⁵ K⁻¹
Coefficient of volume expansion for Water, = 2.1 x 10⁻⁴ K⁻¹
The apparent Coefficient of volume expansion for Water, γ = 2.1 x 10⁻⁴ K⁻¹ - 2.7 x 10⁻⁵ K⁻¹ = 1.83 × 10⁻⁴ K⁻¹
Change in temperature, ΔΘ = Final Temperature - Initial Temperature = 293K - 373K = -80K
Now, the Coefficient of volume expansion is given as:
[tex]\Delta V = -{\gamma}{V \Delta \theta}\\[/tex]
where,
V = initial Volume
ΔV = change in the volume
Thus,
[tex]\Delta V = -{1.83\times 10^{-4} K^{-1} }\times {V \times -80K}\\[/tex]
or
[tex]\Delta V = 146.4\times 10^{-4}\times V[/tex]
or
[tex]\frac{\Delta V}{V} = 146.4\times 10^{-4}[/tex]
Multiplying both sides by 100
we get
[tex]\frac{\Delta V}{V}\times 100 = 146.4\times 10^{-4}\times 100[/tex]
or
change in volume with respect to the initial volume = 1.464%
thus, 1.464 % of the original volume water can be added.
