The apparent coefficient of expansion of a li | vedclass

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(B) The coefficient of real expansion of a liquid $(\gamma_r)$ is related to the apparent coefficient of expansion $(\gamma_a)$ and the coefficient of

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$\frac{X+3 \alpha-Y}{3}$

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(B) The coefficient of real expansion of a liquid $(\gamma_r)$ is related to the apparent coefficient of expansion $(\gamma_a)$ and the coefficient of volume expansion of the vessel $(\gamma_v)$ by the relation: $\gamma_r = \gamma_a + \gamma_v$.Let $\gamma_L$ be the coefficient of real volume expansion of the liquid.For the brass vessel: $\gamma_L = X + 3\alpha$, where $3\alpha$ is the coefficient of volume expansion of brass.For the tin vessel: $\gamma_L = Y + 3\alpha_{	ext{tin}}$, where $\alpha_{	ext{tin}}$ is the coefficient of linear expansion of tin.Equating the two expressions for $\gamma_L$:$X + 3\alpha = Y + 3\alpha_{	ext{tin}}$Rearranging to solve for $\alpha_{	ext{tin}}$:$3\alpha_{	ext{tin}} = X + 3\alpha - Y$$\alpha_{	ext{tin}} = \frac{X + 3\alpha - Y}{3}$

The apparent coefficient of expansion of a liquid when heated in a brass vessel is $X$ and when heated in a tin vessel is $Y$. If $\alpha$ is the coefficient of linear expansion for brass, the coefficient of linear expansion of tin is ..........

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