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(C) The coefficient of real expansion $(\gamma_r)$ of a liquid is defined as the sum of the coefficient of apparent expansion $(\gamma_a)$ and the coe

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$\gamma_r=3 \alpha_g+\gamma_a$

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(C) The coefficient of real expansion $(\gamma_r)$ of a liquid is defined as the sum of the coefficient of apparent expansion $(\gamma_a)$ and the coefficient of volume expansion of the container $(\gamma_g)$.Mathematically,this is expressed as: $\gamma_r = \gamma_a + \gamma_g$.We know that the coefficient of volume expansion $(\gamma_g)$ is three times the coefficient of linear expansion $(\alpha_g)$ for a solid material,i.e.,$\gamma_g = 3\alpha_g$.Substituting this into the first equation,we get: $\gamma_r = \gamma_a + 3\alpha_g$.

The relation between the coefficient of real expansion $(\gamma_r)$ and coefficient of apparent expansion $(\gamma_a)$ of a liquid and the coefficient of linear expansion $(\alpha_g)$ of the material of the container is

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