Question

The apparent coefficient of expansion of a liquid when heated in a copper vessel is \( C \) and in a silver vessel is \( S \). If \( A \) is the linear coefficient of expansion of copper, then the linear coefficient of expansion of silver is

• A. \( \frac{C - S - 3A}{3} \)
• B. \( \frac{C + 3A - S}{3} \)
• C. \( \frac{S + 3A - C}{3} \)
• D. \( \frac{C + S + 3A}{3} \)

Hint:

Expansion: \begin{itemize} \item Volume coefficient ≈ 3 × linear coefficient. \end{itemize}

Answer 1

The Correct Option is B

Concept: Apparent expansion: \[ \gamma_{app} = \gamma_{real} - \gamma_{vessel} \] For solids: \[ \gamma_{vessel} = 3\alpha \] Step 1: {\color{red}For copper vessel.} \[ C = \gamma - 3A \Rightarrow \gamma = C + 3A \] Step 2: {\color{red}For silver vessel.} \[ S = \gamma - 3\alpha_s \] Step 3: {\color{red}Substitute \( \gamma \).} \[ S = C + 3A - 3\alpha_s \] Step 4: {\color{red}Solve.} \[ \alpha_s = \frac{C + 3A - S}{3} \]