The apparent coefficient of expansion of a li | vedclass

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Question

(B) The relationship between the real coefficient of expansion $(\gamma_r)$,apparent coefficient of expansion $(\gamma_a)$,and the volume coefficient

Vedclass · Accepted Answer

$\frac{C + 3A - S}{3}$

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(B) The relationship between the real coefficient of expansion $(\gamma_r)$,apparent coefficient of expansion $(\gamma_a)$,and the volume coefficient of expansion of the vessel $(\gamma_v)$ is given by: $\gamma_r = \gamma_a + \gamma_v$.Since the volume coefficient of expansion $\gamma_v = 3\alpha$,where $\alpha$ is the linear coefficient of expansion,we have $\gamma_r = \gamma_a + 3\alpha$.For the copper vessel: $\gamma_r = C + 3A$.For the silver vessel: $\gamma_r = S + 3\alpha_{Ag}$,where $\alpha_{Ag}$ is the linear coefficient of expansion of silver.Since the real coefficient of expansion of the liquid is constant,we equate the two expressions: $C + 3A = S + 3\alpha_{Ag}$.Rearranging for $\alpha_{Ag}$: $3\alpha_{Ag} = C + 3A - S$.Therefore,$\alpha_{Ag} = \frac{C + 3A - S}{3}$.

The apparent coefficient of expansion of a liquid when heated in a copper vessel is $C$ and when heated in a silver vessel is $S$. If $A$ is the linear coefficient of expansion of copper,then the linear coefficient of expansion of silver is

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