Questions

The figure shows a glass tube (linear co-efficient of expansion is $α$ ) completely filled with a liquid of volume expansion co-efficient $γ$ . On heating length of the liquid column does not change. Choose the correct relation between $γ$ and $α$

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By Expert Faculty of Sri Chaitanya

γ=α

γ=2α

γ=3α

γ=α3

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detailed solution

Correct option is B

When length of the liquid column remains constant, then the level of liquid moves down with respect to the container, thus γ must be less than 3α.Now we can write V=V0(1+γΔT)Since V=Al0=A0(1+2αΔT)l0=V0(1+2αΔT)Hence V0(1+γΔT)=V0(1+2αΔT)⇒γ=2α

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A glass vessel is partially filled with mercury and when both are heated together, the volume of the unfilled part of vessel remains constant at all temperature. Find the initial volume (in cm³) of mercury if the empty part measures 34 cm³ $[Given: α_{vessel} = 9 \times 10^{- 6} /^{\circ} C$ $γ_{Hg} = 18 \times 10^{- 5} /^{\circ} C]$