First slide

Thermal expansion

Question

A 2 litre glass flask contains some mercury. It is found that at all temperatures, the volume of air inside the flask, remains the same. The volume of mercury inside the flask is $(α for glass = 9 \times 10^{- 6} /^{0} C),$ and for mercury = $1 .8 \times 10^{- 4} /^{0} C)$

Moderate

A

1500 cc
B

150 cc
C

3000 cc
D

300 cc

Solution

Since volume of air in the flask remains the same, the expansion in volume of vessel is exactly equal to the volume Expansion of mercury
$\begin{array}{l} ∴ {ΔV}_{V} = {ΔV}_{m} \\ \Rightarrow V_{V} . γ_{v} . ΔT = V_{m} . γ_{m} . ΔT \end{array}$
$\begin{array}{l} \Rightarrow V_{m} = \frac{V_{v} . γ_{v}}{γ_{m}} = \frac{V_{m} \times 3 α}{γ_{m}} \\ \Rightarrow V_{m} = \frac{2000 \times 3 \times 9 \times 10^{- 6}}{1 .8 \times 10^{- 4}} cc = 300 cc \end{array}$

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