Final answer:
To ensure the vacant space in the glass container remains constant with temperature changes, with the volume expansion coefficient of the liquid being four times that of glass, the liquid should occupy 1/5 or 20% of the container's volume.
Step-by-step explanation:
The student's question pertains to the volume expansion of substances when subjected to variations in temperature. Specifically, it deals with a scenario where both a glass container and a viscous liquid within are expanding, and it asks for the fraction of the container the liquid should occupy so that the volume of the remaining vacant space in the container remains constant regardless of temperature changes.
The coefficient of volume expansion for the glass is given as one quarter of that for the liquid. To ensure the remaining vacant space in the container is constant at all temperatures, we need to account for the expansion ratios. Let the volume expansion coefficients be α for glass and 4α for the liquid. Given a container of volume V, if we fill it with liquid volume L and leave a space S, we have L + S = V. When the temperature changes, we want the space to remain the same, so αV = 4αL. Simplifying gives us L = V/5. Thus, the liquid should occupy 1/5 or 20% of the container's volume to achieve the desired result.