表面張力是液體表面像一層「彈性薄膜」的性質。液體分子互相吸引，表面的分子被往內拉，使表面盡量縮小。Surface tension makes a liquid surface act like an "elastic film." Molecules pull inward, making the surface as small as possible.
符號：σ（sigma） 單位：N/mSymbol: σ (sigma) · Unit: N/m
水的 σ ≈ 0.072 N/m；香檳的 σ ≈ 0.05 N/m。Water: σ ≈ 0.072 N/m · Champagne: σ ≈ 0.05 N/m
當液體表面彎曲時（例如氣泡），表面張力會對內部產生額外的壓力。When a liquid surface is curved (e.g., a bubble), surface tension creates extra pressure inside.
a 是氣泡半徑（m）。圓柱面則是 ΔP = σ / a。a is the bubble radius (m). For a cylindrical surface, ΔP = σ / a.
Pb：氣泡內部壓力（Pa）
P0：液體外部壓力（Pa）
σ：表面張力（N/m）
a：氣泡半徑（m）Pb: internal bubble pressure (Pa) · P0: liquid pressure (Pa) · σ: surface tension (N/m) · a: radius (m)
因為 a 在分母：a 越小 → 2σ/a 越大。Because a is in the denominator: smaller a → larger 2σ/a.
半徑減半 → 拉普拉斯壓力加倍。Halve the radius → double the Laplace pressure.
| 換算 Conversion | 結果 Result |
|---|---|
| 1 mm | 10⁻³ m |
| 1 cm | 10⁻² m |
| 1 Pa | 1 N/m² |
⚠️ 計算前，半徑一定要換成米（m）！Before calculating, always convert radius to metres (m)!
看圖判斷：哪個氣泡的內部壓力更大？Look and decide: Which bubble has higher internal pressure?
把碎片拼成正確的拉普拉斯壓力公式：Arrange the pieces to form the correct Laplace pressure formula:
Pb = P0 + 2σ / a
代入數值，計算氣泡內部壓力 Pb。Plug in the values and calculate the bubble's internal pressure Pb.
表面張力 σ = 0.05 N/m Surface tension
液體壓力 P0 = 101325 Pa Liquid pressure
氣泡半徑 a = 0.5 mm = 5×10⁻⁴ m Bubble radius
求 Pb = ?
已知 Pb − P0 = 400 Pa Pressure difference
σ = 0.05 N/m Surface tension
求 a = ?
比較兩個氣泡的內部壓力，並計算壓力差。Compare the internal pressure of two bubbles and calculate the pressure difference.
aA = 1 mm = 10⁻³ m
aB = 0.5 mm = 5×10⁻⁴ m
σ = 0.05 N/m，P0 = 101325 Pa
孩子當「出題科學家」，設計一道氣泡壓力題考家長！Child becomes the "Question Scientist" and creates a bubble pressure problem to challenge the parent!
要求：指定半徑、表面張力、液體壓力 ·