An ordinary glass is filled to the brim with water at 100oc. how much water could be added to the glass if the temperature is lowered to 20oc? assume that the coefficient of volume expansion for glass is 2.7 x 10-5 k-1 and for water it is 2.1 x 10-4 k-1

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:

where,

V = initial Volume

ΔV = change in the volume

Thus,

or

or

Multiplying both sides by 100

we get

or

change in volume with respect to the initial volume = 1.464%

thus, 1.464 % of the original volume water can be added.

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