Thermal Expansion

We are asked to find the linear coefficient of expansion of silver given the apparent coefficient of expansion of a liquid when heated in copper and silver vessels. The apparent coefficient of expansion of a liquid, when placed in a container, depends on the coefficient of expansion of both the liquid and the container. Specifically, the apparent coefficient of expansion of the liquid in a copper vessel and in a silver vessel are influenced by both the liquid's expansion and the container's expansion. The formula for the apparent coefficient of expansion when the liquid is in a vessel with a material having a coefficient of linear expansion is: Where: - is the apparent coefficient of expansion of the liquid in the vessel, - is the coefficient of expansion of the liquid, - is the coefficient of expansion of the vessel material.
Step 1: Apparent Coefficient of Expansion in Copper and Silver Vessels - The apparent coefficient of expansion of the liquid in a copper vessel is given by: where is the coefficient of linear expansion of copper, and is the coefficient of expansion of the liquid. - The apparent coefficient of expansion of the liquid in a silver vessel is given by: where is the coefficient of linear expansion of silver.
Step 2: Solving for the Coefficient of Expansion of Silver We now have the following system of equations: 1. 2. To find , subtract the first equation from the second: This gives: Thus, the linear coefficient of expansion of silver is: Therefore, the correct answer is: