A liquid when heated in a copper vessel and when heated in a...

A liquid when heated in a copper vessel and when heated in a silver vessel, the apparent coefficient of expansion is ' $C^{\prime}$ and ' $S^{\prime}$, respectively. If coefficients of linear expansion of copper is ' $A^{\prime}$, then coefficient of linear expansion of silver is : (a) $\frac{C+S-3 A}{3}$ (b) $\frac{C+3 A-S}{3}$ (c) $\frac{3 A-S-C}{3}$ (d) $\frac{C+S+3 A}{3}$

A liquid when heated in a copper vessel and when heated in a silver vessel, the apparent coefficient of expansion is ' $C^{\prime}$ and ' $S^{\prime}$, respectively. If coefficients of linear expansion of copper is ' $A^{\prime}$, then coefficient of linear expansion of silver is :
(a) $\frac{C+S-3 A}{3}$
(b) $\frac{C+3 A-S}{3}$
(c) $\frac{3 A-S-C}{3}$
(d) $\frac{C+S+3 A}{3}$

Key Concepts

Apparent vs True Expansion Measurements

When measuring the expansion of a liquid confined within a container, the container's expansion interferes with the observed change in volume. The apparent coefficient of expansion of the liquid is influenced by both the true expansion of the liquid and the expansion of the container walls. Correcting for this effect requires consideration of the container’s expansion coefficient, which is typically associated with its material properties, such as the coefficient of linear expansion for metals.

Coefficient of Volume Expansion

The coefficient of volume expansion describes the relative change in volume of a substance as a function of temperature change. For liquids, this coefficient is used to determine how much a liquid expands or contracts when heated or cooled. Understanding volume expansion is essential in applications where precision is required, as the container’s expansion may influence the observed or apparent expansion of the liquid within.

Thermal Expansion

Thermal expansion refers to the tendency of matter to change in volume or shape in response to a change in temperature. This fundamental concept applies to all materials, including liquids and solids, and is governed by their intrinsic properties. When heated, most materials expand, and the degree of expansion is quantified through specific coefficients that relate the change in volume or length to the change in temperature.

Coefficient of Linear Expansion

The coefficient of linear expansion is a material-specific constant that quantifies the change in length per unit length for a given temperature change. It is particularly important for solids, such as metals, where dimensional changes due to temperature variation can significantly affect structural behavior and measurement accuracy. This concept is crucial when dealing with systems that involve interactions between different materials with varying expansion rates.

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