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(D) The coefficient of real expansion of a liquid $(\gamma_r)$ is constant and is given by the sum of the coefficient of apparent expansion $(\gamma_a

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$12 	imes 10^{-6} /{ }^{\circ} C$

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(D) The coefficient of real expansion of a liquid $(\gamma_r)$ is constant and is given by the sum of the coefficient of apparent expansion $(\gamma_a)$ and the coefficient of volume expansion of the container $(\gamma_v = 3\alpha$, where $\alpha$ is the coefficient of linear expansion). Thus, $\gamma_r = \gamma_{a1} + 3\alpha_1 = \gamma_{a2} + 3\alpha_2$. Given: $\gamma_{a1} = 6 	imes 10^{-6} /{ }^{\circ} C$ (for copper vessel) $\alpha_1 = 18 	imes 10^{-6} /{ }^{\circ} C$ (for copper) $\gamma_{a2} = 24 	imes 10^{-6} /{ }^{\circ} C$ (for steel vessel) Substituting the values: $6 	imes 10^{-6} + 3(18 	imes 10^{-6}) = 24 	imes 10^{-6} + 3\alpha_2$ $6 	imes 10^{-6} + 54 	imes 10^{-6} = 24 	imes 10^{-6} + 3\alpha_2$ $60 	imes 10^{-6} = 24 	imes 10^{-6} + 3\alpha_2$ $3\alpha_2 = 36 	imes 10^{-6} /{ }^{\circ} C$ $\alpha_2 = 12 	imes 10^{-6} /{ }^{\circ} C$.

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