The coefficient of apparent expansion of merc | vedclass

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(A) The real coefficient of volume expansion of mercury $(\gamma_{	ext{real}})$ is constant regardless of the vessel used.The relationship between re

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$9 	imes 10^{-6} /{ }^{\circ} C$

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(A) The real coefficient of volume expansion of mercury $(\gamma_{	ext{real}})$ is constant regardless of the vessel used.The relationship between real expansion, apparent expansion, and vessel expansion is given by:$\gamma_{	ext{real}} = \gamma_{	ext{app}} + \gamma_{	ext{vessel}}$Since $\gamma_{	ext{real}}$ is the same for both cases:$(\gamma_{	ext{app}} + \gamma_{	ext{vessel}})_{	ext{glass}} = (\gamma_{	ext{app}} + \gamma_{	ext{vessel}})_{	ext{steel}}$We know that the volume expansion coefficient of a solid is $\gamma_{	ext{vessel}} = 3\alpha$.For steel:$\gamma_{	ext{vessel, steel}} = 3 	imes (12 	imes 10^{-6} /{ }^{\circ} C) = 36 	imes 10^{-6} /{ }^{\circ} C$Substituting the values into the equation:$153 	imes 10^{-6} + \gamma_{	ext{vessel, glass}} = 144 	imes 10^{-6} + 36 	imes 10^{-6}$$153 	imes 10^{-6} + \gamma_{	ext{vessel, glass}} = 180 	imes 10^{-6}$$\gamma_{	ext{vessel, glass}} = (180 - 153) 	imes 10^{-6} = 27 	imes 10^{-6} /{ }^{\circ} C$Since $\gamma_{	ext{vessel, glass}} = 3\alpha_{	ext{glass}}$:$3\alpha_{	ext{glass}} = 27 	imes 10^{-6} /{ }^{\circ} C$$\alpha_{	ext{glass}} = 9 	imes 10^{-6} /{ }^{\circ} C$

The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6} /{ }^{\circ} C$ and in a steel vessel is $144 \times 10^{-6} /{ }^{\circ} C$. If $\alpha$ for steel is $12 \times 10^{-6} /{ }^{\circ} C$, then the coefficient of linear expansion $\alpha$ for glass is:

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