Question

During an all-night cram session, a student heats up a one-half liter (0.50 x 10- 3 m3) glass (Pyrex) beaker of cold coffee. Initially, the temperature is 18 °C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to 92 °C. The coefficient of volume expansion of coffee is the same as that of water. How much coffee (in cubic meters) has spilled out of the beak?

Answer 1

Δ
`V_(c)` = 7.415 10⁻⁶ m³ (7.415 10⁻³ L)

Step-by-step explanation:

This problem must find the change in volume of coffee and pyrex, the expression

ΔV = V₀ β ΔT

The expansion coefficients are

Water Volumetry β = 207 10⁻⁶ C⁻¹

Pyrex Linear α = 3.2 10⁻⁶ C⁻¹

In general, for solids the solids find the linear expansion coefficient tabulated, but the linear volumetric coefficient is related

β = 3 α

Let's calm the volume change for the pyrex glass

Δ
`V_(p)` = V₀ 3α ΔT

Δ
`V_(p)`= 0.50 10⁻³ 3 3.2 10⁻⁶ (92-18)

Δ
`V_(p)` = 3.552 10⁻⁷ m³

We look for the change in volume for coffee that is equal to that of water

Δ
`V_(w)` = 0.50 10⁻³ 210 10⁻⁶ (92-18)

Δ
`V_(w)` = 7.77 10⁻⁶ m³

The amount of spilled coffee is the difference in volumes

Δ
`V_(c)` = Δ
`V_(w)` - Δ
`V_(p)`

Δ
`V_(c)` = 7.77 10⁻⁶ - 3.552 10⁻⁷

Δ
`V_(c)` = 7.415 10⁻⁶ m³

Let's reduce to liters

Δ
`V_(c)` = 7.415 10⁻⁶ m³ (1000 L / 1 m3)

ΔΔ
`V_(c)` = 7.415 10⁻³ L