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If V is the volume of the vessel and $V_{L}$ is volume of liquid to be taken for the free space volume to be constant at all temperatures then

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VγR=VLγg

VLγg=VγR

VLγR=Vγg

Vγg=VLγR

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detailed solution

Correct option is D

change in volume of glass = change in volume of liquid ΔVg=ΔVL---(1) in terms of coefficient of volume expansion of glass γg and coefficient of real expansion of liquid γR ; Δt change in temperature ; from γ=ΔVVΔt we get, from eqn(1) VγgΔt=VLγRΔt Vγg=VLγR

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