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(D) The coefficient of real expansion of a liquid $(\gamma_{	ext{real}})$ is constant for a given liquid. The relationship between real expansion, ap

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

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(D) The coefficient of real expansion of a liquid $(\gamma_{	ext{real}})$ is constant for a given liquid. The relationship between real expansion, apparent expansion $(\gamma_{	ext{app}})$, and the volume expansion of the vessel $(\gamma_{	ext{vessel}})$ is given by: $\gamma_{	ext{real}} = \gamma_{	ext{app}} + \gamma_{	ext{vessel}}$.For vessel $A$, the coefficient of volume expansion is $\gamma_A = 3\alpha$. Thus, $\gamma_{	ext{real}} = \gamma_1 + 3\alpha$.For vessel $B$, let the coefficient of linear expansion be $\alpha_B$. Then $\gamma_B = 3\alpha_B$. Thus, $\gamma_{	ext{real}} = \gamma_2 + 3\alpha_B$.Since $\gamma_{	ext{real}}$ is the same in both cases, we equate them: $\gamma_1 + 3\alpha = \gamma_2 + 3\alpha_B$.Solving for $\alpha_B$: $3\alpha_B = \gamma_1 - \gamma_2 + 3\alpha$.Therefore, $\alpha_B = \frac{\gamma_1 - \gamma_2}{3} + \alpha$.

The coefficients 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 the vessel $A$ is $\alpha$, the coefficient of linear expansion of the vessel $B$ is

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