In this scenario, we explore the thermal expansion of a glass flask filled with mercury when the temperature is increased from 0 degrees Celsius to 100 degrees Celsius. Both the glass and the mercury expand, but they do not expand equally due to their different coefficients of volumetric expansion, denoted as β (beta). The coefficient for mercury is greater than that for glass, which leads to a situation where the mercury overflows from the flask.

To quantify the overflow, we define the change in volume for both substances. The change in volume for the mercury, denoted as ΔV_mercury, can be expressed using the formula:

ΔV_mercury = β_mercury × V_initial × ΔT

Similarly, the change in volume for the glass is given by:

ΔV_glass = β_glass × V_initial × ΔT

Here, V_initial is the initial volume of both the glass and the mercury, which is 250 cm³, and ΔT is the change in temperature, which is 100 degrees Celsius.

The volume of mercury that spills out, denoted as V_spill, is calculated by subtracting the change in volume of the glass from that of the mercury:

V_spill = ΔV_mercury - ΔV_glass

Substituting the expressions for ΔV, we have:

V_spill = (β_mercury - β_glass) × V_initial × ΔT

Plugging in the values, we find:

V_spill = 250 cm³ × 100 × (1.8 × 10^-4 - 1.2 × 10^-5)

Calculating this gives us a result of V_spill = 4.2 cm³. This positive value indicates that indeed, some mercury will spill out of the flask when the temperature is raised, confirming our understanding of thermal expansion in different materials.

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