The apparent coefficient of expansion of a liquid, when heated in a copper vessel is C and when heated in silver vessel is S. If A is linear coefficient of expansion of copper, then linear coefficient of expansion of silver is
\(\dfrac{C+3A-S}{3}\)
The real (absolute) expansion of a liquid equals its apparent expansion plus the volume expansion of the vessel, and the volume expansion coefficient of a solid is three times its linear coefficient. The real coefficient of the liquid is the same whichever vessel is used.
Step 1 — Relation: \(\gamma_{\text{real}}=\gamma_{\text{app}}+\gamma_{\text{vessel}}\).
Step 2 — Copper vessel (γ = 3A): \(\gamma_{\text{real}}=C+3A\).
Step 3 — Silver vessel with linear coefficient αs: \(\gamma_{\text{real}}=S+3\alpha_s\).
Step 4 — Equating the two: \(\alpha_s=\dfrac{C+3A-S}{3}\).
The expressions (C − S − 3A)/3 and (S + 3A − C)/3 reverse the signs of some of the terms obtained from equating the real coefficients, and (C + S + 3A)/3 adds both apparent coefficients, which has no basis in the relation between real and apparent expansion.
\(\dfrac{C+3A-S}{3}\) option is correct.
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