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2 months ago

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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. Ini

tially, 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?

1 answer:

serg [3.5K]2 months ago

8 0

Answer:

Δ $V_{c}$ = 7.415 10⁻⁶ m³ (7.415 10⁻³ L)

Explanation:

This problem seeks to calculate the change in volume of coffee and pyrex with the expression

ΔV = V₀ β ΔT

The coefficients for expansion are

Water Volumetry β = 207 10⁻⁶ C⁻¹

Pyrex Linear α = 3.2 10⁻⁶ C⁻¹

In general, for solids, the linear expansion coefficients are cited, but the volumetric coefficient is linked to

β = 3 α

Now, let’s compute the volume change for 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

For the change in volume of coffee, which is equivalent 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 spilled coffee amount represents the difference in the respective 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

To convert to liters

Δ $V_{c}$ = 7.415 10⁻⁶ m³ (1000 L / 1 m³)

Δ $V_{c}$ = 7.415 10⁻³ L

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Refer to the attached diagram for enhanced clarity regarding the question.

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