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? (βglass = 1.2 × 10-5 / K & γwater = 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
ΔV1 = 250(1 + γl θ) – 250 = 250 γl θ
If the bottle (glass) expands:
volume of water over flown ΔV2 = 250(γl – γg)θ ,
where γg = 3β/2 = 1.8 × 10-5/°C
= 250 (58.2 × 10-5) × (60 – 50) = 1.455 cm³