The coefficient of apparent expansion of a li | vedclass

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Question

(D) The coefficient of real expansion of a liquid $(\gamma_{	ext{real}})$ is related to the coefficient of apparent expansion $(\gamma_{	ext{app}})$

Vedclass · Accepted Answer

$\frac{\gamma_1 - \gamma_2}{3} + \alpha$

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(D) The coefficient of real expansion of a liquid $(\gamma_{	ext{real}})$ is related to the coefficient of apparent expansion $(\gamma_{	ext{app}})$ and the coefficient of volume expansion of the vessel $(\gamma_{	ext{vessel}})$ by the formula: $\gamma_{	ext{real}} = \gamma_{	ext{app}} + \gamma_{	ext{vessel}}$.Since $\gamma_{	ext{vessel}} = 3\alpha$ (where $\alpha$ is the coefficient of linear expansion),we have $\gamma_{	ext{real}} = \gamma_{	ext{app}} + 3\alpha$.For vessel $A$: $\gamma_{	ext{real}} = \gamma_1 + 3\alpha$.For vessel $B$: $\gamma_{	ext{real}} = \gamma_2 + 3\alpha_B$,where $\alpha_B$ is the coefficient of linear expansion of vessel $B$.Since the liquid is the same,$\gamma_{	ext{real}}$ is constant. Therefore: $\gamma_1 + 3\alpha = \gamma_2 + 3\alpha_B$.Rearranging for $\alpha_B$: $3\alpha_B = \gamma_1 - \gamma_2 + 3\alpha$.Dividing by $3$: $\alpha_B = \frac{\gamma_1 - \gamma_2}{3} + \alpha$.

The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$ respectively. If the coefficient of linear expansion of vessel $A$ is $\alpha$,the coefficient of linear expansion of vessel $B$ is

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