A 100-m L gradusted cylinder is made from Pyrex glass and...

A $100-m L$ gradusted cylinder is made from Pyrex glass and contains $50.000 \mathrm{~mL}$ of water at $50^{\circ} \mathrm{C}$. If the temperature of the water and the cylinder is raised by exactly $25^{\circ} \mathrm{C}$, what will the cylinder measure for the new volume of water? Do not neglect thermal expansion of the cylinder itself, but do neglect variations in the expansion coefficients with temperature.

Key Concepts

Combined Effects in Measurement

When measuring the volume of a substance in a container, both the expansion of the substance and the container must be considered. The net change in the measured volume is determined by the individual expansion characteristics of the fluid (volumetric expansion) and the container (linear expansion), which can lead to a difference between the actual and the observed volume after heating.

Coefficient of Volumetric Thermal Expansion

The coefficient of volumetric thermal expansion measures the rate at which a material's volume changes with a rise in temperature. It is crucial for fluids, as it determines how much a fluid expands when heated, independent of the container effects.

Thermal Expansion

Thermal expansion is the phenomenon wherein materials change their dimensions (length, area, or volume) in response to a change in temperature. When heated, most materials expand due to the increased kinetic energy of their particles, and this expansion must be taken into account when both the container and its contents are subject to temperature changes.

Coefficient of Linear Thermal Expansion

The coefficient of linear thermal expansion quantifies how a material's length changes with temperature. It is particularly relevant for solids such as container walls, where changes in length directly affect the overall dimensions and, consequently, the calibration of measurement devices.

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