Q: A 250 cm³ glass bottle is completely filled with water at 50°C. The bottle and water are heated to 60°C. How much water runs over If : (a) The expansion of bottle is neglected (b) the expansion of bottle is included? (β_{glass} = 1.2 × 10^{-5} / K & γ_{water} = 60 × 10^{-5} / °C)

Sol: Water overflow = (final volume of water) – (final volume of bottle)

If the expansion of bottle is neglected: volume of water over flown

ΔV_{1} = 250(1 + γ_{l} θ) – 250 = 250 γ_{l} θ

If the bottle (glass) expands:

volume of water over flown ΔV_{2} = 250(γ_{l} – γ_{g})θ ,

where γ_{g} = 3β/2 = 1.8 × 10^{-5}/°C

= 250 (58.2 × 10^{-5}) × (60 – 50) = 1.455 cm³