Final answer:
The student's question pertains to finding the fraction of a glass vessel to be filled with mercury to ensure that upon heating, the volume of the empty vessel does not change. This requires equating the thermal expansion of mercury to that of glass and solving for the fractional volume of mercury required.
Step-by-step explanation:
The student is asking about thermal expansion, specifically how to fill a glass vessel with mercury so that when the system is heated, the volume of the empty vessel remains constant. This problem requires an understanding of the coefficients of thermal expansion for glass and mercury, as well as the ability to equate the expansion of mercury to the corresponding expansion of the glass vessel.
To solve this, you need to set up an equation that matches the volume expansion of mercury with the volume expansion of the glass. Let αg represent the coefficient of thermal expansion for glass, and αm for mercury. Let V be the total volume of the vessel and xV be the volume occupied by mercury, where x is the fraction we want to find. As both the glass and mercury are subjected to the same change in temperature, ΔT, the expansions will be proportional to their volumes and coefficients of thermal expansion. The change in volume for glass should equal the change in volume for mercury for the empty volume to remain the same:
αgV(1 - x)ΔT = αmxVΔT
Cancelling out common terms, the fraction x can be found with:
x = αg/(αg + αm)
Since we have ignored other factors such as capillary action, this solution is based on the assumption of linear and uniform expansion of materials.