A 1 L glass flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. What is the volume (in cc) of mercury in this flask if coefficient of linear expansion of glass is 9 × 10-6/°C while of volume expansion of mercury is 1.8 × 10-4/°C?

Question

A 1 L glass flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. What is the volume (in cc) of mercury in this flask if coefficient of linear expansion of glass is 9 × 10-6/°C while of volume expansion of mercury is 1.8 × 10-4/°C? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

It is given that the volume of air in the flask remains the same. This means that the expansion in volume of the vessel is exactly equal to the volume expansion of mercury,
i.e.,

Δ V_{G} = Δ V_{L}

or

V_{G} γ_{G} Δ θ = V_{L} γ_{L} Δ θ

∴ V_{L} = \frac{V _{G} γ _{G}}{γ _{L}}

= \frac{1000 \times ( 3 \times 9 \times 1 0 ^{- 6} )}{1.8 \times 1 0 ^{- 4}}

= 150 cc