Solveeit Logo
Login

Question

Question: The coefficient of apparent expansion of a liquid in a copper vessel is *C* and in a silver vessel *...

The coefficient of apparent expansion of a liquid in a copper vessel is C and in a silver vessel S. The coefficient of volume expansion of copper is γC\gamma_{C}. What is the coefficient of linear expansion of silver

A

(C+γC+S)/3(C + \gamma_{C} + S)/3

B

(C−γC+S)/3(C - \gamma_{C} + S)/3

C

(C+γC−S)/3(C + \gamma_{C} - S)/3

D

(C−γC−S)/3(C - \gamma_{C} - S)/3

Answer

(C+γC−S)/3(C + \gamma_{C} - S)/3

Explanation

Solution

Apparent coefficient of volume expansion for liquid γapp=γL−γs\gamma_{app} = \gamma_{L} - \gamma_{s} ∴ γL=γapp+γs\gamma_{L} = \gamma_{app} + \gamma_{s}

where γs is coefficient of volume expansion for solid vessel.

When liquid is placed in copper vessel then γL = C + γcopper (i)

[As γapp. for liquid in copper vessel = C]

When liquid is placed in silver vessel then γL = S + γsilver....(ii)

[As γapp. for liquid in silver vessel = S]

From equation (i) and (ii) we get C + γcopper = S + γsilver

∴ γsilver=C+γcopper−S\gamma_{silver} = C + \gamma_{copper} - S

Coefficient of volume expansion = 3 × Coefficient of linear expansion

⇒ αsilver=γsilver3=C+γcopper−S3\alpha_{\text{silver}} = \frac{\gamma_{\text{silver}}}{3} = \frac{C + \gamma_{\text{copper}} - S}{3}