First slide

Thermal expansion

Question

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

Moderate

A

$V γ_{R} = V_{L} γ_{g}$
B

$V_{L} γ_{g} = \frac{V}{γ_{R}}$
C

$\frac{V_{L}}{γ_{R}} = \frac{V}{γ_{g}}$
D

$V γ_{g} = V_{L} γ_{R}$

Solution

$c h a n g e i n v o l u m e o f g l a s s = c h a n g e i n v o l u m e o f l i q u i d Δ V_{g} = Δ V_{L} - - - (1) i n t e r m s o f c o e f f i c i e n t o f v o l u m e e x p a n s i o n o f g l a s s γ_{g} a n d c o e f f i c i e n t o f r e a l e x p a n s i o n o f l i q u i d γ_{R}; Δ t c h a n g e i n t e m p e r a t u r e; f r o m γ = \frac{Δ V}{V Δ t} w e g e t, f r o m e q n (1) V γ_{g} Δ t = V_{L} γ_{R} Δ t V γ_{g} = V_{L} γ_{R}$

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