Final answer:
When the temperature of glycerin in an aluminum cup is increased from 22 °C to 28 °C, 3.06 cm³ of glycerin will spill out of the cup due to thermal expansion.
Step-by-step explanation:
The student's question regards the concept of thermal expansion, specifically concerning an aluminum cup filled with glycerin. When the temperature of both the cup and the glycerin is increased from 22 °C to 28 °C, we can assume that both materials expand, but since we're ignoring the expansion of the aluminum cup, we only need to focus on the expansion of glycerin.
The formula to calculate the volume expansion of a liquid is given by ΔV = βVΔT, where ΔV is the change in volume, β is the coefficient of volume expansion, V is the initial volume, and ΔT is the change in temperature.
For the glycerin, ΔV = (5.1 × 10⁻⁴ /°C) × 100 cm³ × (28 °C - 22 °C). By calculating this, we find that the glycerin's volume increases by 3.06 cm³. Therefore, 3.06 cm³ of glycerin will spill out of the cup.