A glass flask of volume at is completely filled with a liquid having a real volume expansivity of . If the linear expansivity of the glass is , what volume of the liquid (in ) will overflow when the flask and its contents are heated to ?
Answer: 18.8 cm^3
Answer
18.8 cm^3
The volume of liquid that overflows is equal to the apparent increase in volume of the liquid. The apparent volume expansivity of the liquid \(\gamma_a\) is given by \(\gamma_a = \gamma_r - \gamma_v\), where \(\gamma_r = 5.0 \times 10^{-4}\text{ K}^{-1}\) is the real expansivity of the liquid, and \(\gamma_v = 3\alpha = 3 \times 1.0 \times 10^{-5} = 0.3 \times 10^{-4}\text{ K}^{-1}\) is the volume expansivity of the glass flask. Therefore, \(\gamma_a = 5.0 \times 10^{-4} - 0.3 \times 10^{-4} = 4.7 \times 10^{-4}\text{ K}^{-1}\). The overflow volume is \(\Delta V_a = V_0 \times \gamma_a \times \Delta T = 800 \times (4.7 \times 10^{-4}) \times 50 = 18.8\text{ cm}^3\).
Step-by-Step Solution
Key Concept
Real and apparent cubic expansivity of liquids