A glass vessel of volume V_0 is completely fi | vedclass

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(A) The volume of the liquid that overflows is equal to the difference between the expansion of the liquid and the expansion of the glass vessel.Incre

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$V_0 \Delta T(\gamma_L - 3\alpha_g)$

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(A) The volume of the liquid that overflows is equal to the difference between the expansion of the liquid and the expansion of the glass vessel.Increase in volume of liquid,$\Delta V_L = V_0 \gamma_L \Delta T$.Increase in volume of the glass vessel,$\Delta V_g = V_0 \gamma_g \Delta T$.Since the coefficient of volume expansion $\gamma_g = 3\alpha_g$,we have $\Delta V_g = V_0 (3\alpha_g) \Delta T$.The volume of liquid that overflows is $\Delta V_{overflow} = \Delta V_L - \Delta V_g$.$\Delta V_{overflow} = V_0 \gamma_L \Delta T - V_0 (3\alpha_g) \Delta T$.$\Delta V_{overflow} = V_0 \Delta T (\gamma_L - 3\alpha_g)$.

$A$ glass vessel of volume $V_0$ is completely filled with a liquid and its temperature is raised by $\Delta T$. What volume of the liquid will flow over,if the coefficient of linear expansion of glass is $\alpha_g$ and the coefficient of volume expansion of the liquid is $\gamma_L$?

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