The coefficient of cubical expansion of liquid and glass are in the ratio of 8:1. The volume of the liquid to be taken into 800 cc container so that the unoccupied portion remains constant is

10cc

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100cc

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80cc

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8cc

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Solution

The correct option is B 100cc
$γ_{l} = 8 γ_{g}$
$V_{g} = 800 c c$
$V_{g}^{'} = V_{g} (1 + γ_{g} Δ Θ)$
$V_{l}^{'} = V_{l} (1 + γ_{l} Δ Θ)$
Given, $V_{g} - V_{l} = V_{g}^{'} - V_{l}^{'}$
$\Rightarrow V_{g} - V_{l} = (V_{g} - V_{l}) + Δ Θ (V_{g} γ_{g} - V_{l} γ_{l})$
$\Rightarrow V_{l} = \frac{V_{g} γ_{g}}{γ_{l}} = \frac{800}{8} = 100 c c$

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The coefficient of cubical expansion of liquid and glass are in the ratio of 8:1. The volume of the liquid to be taken into 800 cc container so that the unoccupied portion remains constant is

The correct option is B 100ccγl=8γgVg=800ccV′g=Vg(1+γgΔΘ)V′l=Vl(1+γlΔΘ)Given, Vg−Vl=V′g−V′l⇒Vg−Vl=(Vg−Vl)+ΔΘ(Vgγg−Vlγl)⇒Vl=Vgγgγl=8008=100cc