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

Answer:

Δ = 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 = V₀ 3α ΔT

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

                Δ = 3.552 10⁻⁷ m³

For the change in volume of coffee, which is equivalent to that of water

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

                Δ = 7.77 10⁻⁶ m³

The spilled coffee amount represents the difference in the respective volumes

              Δ =  Δ -  Δ

             Δ = 7.77 10⁻⁶ - 3.552 10⁻⁷

              Δ = 7.415 10⁻⁶ m³

To convert to liters

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

             Δ = 7.415 10⁻³ L