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Question: The apparent coefficient of expansion of a liquid when heated in a copper vessel is C and when heate...

The apparent coefficient of expansion of a liquid when heated in a copper vessel is C and when heated 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

C+S−3A3\frac{C + S - 3A}{3}

B

C+3A−S3\frac{C + 3A - S}{3}

C

S+3A−C3\frac{S + 3A - C}{3}

D

C+S+3A3\frac{C + S + 3A}{3}

Answer

C+3A−S3\frac{C + 3A - S}{3}

Explanation

Solution

γr=γa+γv\gamma_{r} = \gamma_{a} + \gamma_{v}; where γr=\gamma_{r} =coefficient of real expansion, γa=\gamma_{a} =coefficient of apparent expansion and γv=\gamma_{v} =coefficient of expansion of vessel.

For copper γr=C+3αCu=C+3A\gamma_{r} = C + 3\alpha_{Cu} = C + 3A

For silver γr=S+3αAg\gamma_{r} = S + 3\alpha_{Ag}

⇒ C+3A=S+3αAgC + 3A = S + 3\alpha_{Ag} ⇒ αAg=C−S+3A3\alpha_{Ag} = \frac{C - S + 3A}{3}