An aluminum can is filled to the brim with a liquid. The can...

An aluminum can is filled to the brim with a liquid. The can and the liquid are heated so their temperatures change by the same amount. The can's initial volume at $5^{\circ} {C}$ is $3.5 \times 10^{-4} {m}^{3} .$ The coefficient of volume expansion for aluminum is $69 \times 10^{-6}({C}^{9})^{-1}$ When the can and the liquid are heated to $78^{\circ} {C}, 3.6 \times 10^{-6} {m}^{3}$ of liquid spills over. What is the coefficient of volume expansion of the liquid?

An aluminum can is filled to the brim with a liquid. The can and the liquid are heated so their temperatures change by the same amount. The can's initial volume at $5^{\circ} {C}$ is $3.5 \times 10^{-4} {m}^{3} .$ The coefficient of volume expansion for aluminum is $69 \times 10^{-6}({C}^{9})^{-1}$
When the can and the liquid are heated to $78^{\circ} {C}, 3.6 \times 10^{-6} {m}^{3}$ of liquid spills over. What is the coefficient of volume expansion of the liquid?

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Key Concepts

Coefficient of Volume Expansion

The coefficient of volume expansion defines how the volume of a material changes with a change in temperature, usually given by the formula ?V = V0??T. It quantifies the proportional change in volume per degree change in temperature and is fundamental when comparing how different materials respond to heating or cooling.

Thermal Expansion in Solids and Liquids

Thermal expansion refers to the tendency of matter to change in volume in response to a change in temperature. Solids and liquids typically have different expansion coefficients, meaning that when both are subjected to the same temperature change, they expand by different amounts. This mismatch can have important outcomes, such as causing liquids to overflow from their containers if the container expands less than the liquid.

Temperature Change and its Impact

The temperature change, calculated as ?T = final temperature - initial temperature, is a key factor in determining the extent of volume expansion. It directly scales the effect of the coefficient of volume expansion on the initial volume, highlighting how crucial accurate temperature measurements are for predicting material behavior under thermal variations.

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