HKDSE Physics – General Gas Law

HKDSE Physics Core
Chapter 4: General Gas Law | 普適氣體定律

Billy Sir’s Smart Notes: Master Boyle’s, Charles’, and Pressure Laws, and the General Gas Equation.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握波義耳、查理、壓力定律及普適氣體方程。

1. Boyle’s Law | 波義耳定律

For a fixed mass of gas at a constant temperature, its pressure is inversely proportional to its volume. 在恆定溫度下，一定質量的氣體，其壓力與體積成反比。

📉 Formula & Experiment | 公式與實驗

$$ P_1 V_1 = P_2 V_2 $$

Experiment Setup: A sealed syringe is connected to a Bourdon gauge (pressure sensor). (實驗裝置：密封注射器連接壓力計。)

Push the plunger slowly to decrease the volume. (緩慢推動柱塞以減少體積。)
Why slowly? To allow heat to escape to the surroundings, ensuring the temperature remains constant. (為什麼要緩慢？讓熱量散失到周圍環境，確保溫度保持不變。)
Result: As volume ($ V $) decreases, pressure ($ P $) increases.

2. Pressure Law | 壓力定律

For a fixed mass of gas at a constant volume, its pressure is directly proportional to its absolute temperature. 在恆定體積下，一定質量的氣體，其壓力與絕對溫度成正比。

🌡️ Formula & Experiment | 公式與實驗

\frac{P_1}{T_1} = \frac{P_2}{T_2}

Experiment Setup: A round-bottom flask of fixed volume is submerged in a water bath, connected to a pressure sensor. (實驗裝置：固定體積的圓底燒瓶浸入水浴中，連接壓力感測器。)

Heat the water bath gradually and record the pressure and temperature. (逐漸加熱水浴並記錄壓力和溫度。)
Ensure the flask is fully submerged so the gas temperature equals the water temperature. (確保燒瓶完全浸沒，使氣體溫度等於水溫。)
Result: As absolute temperature ($ T $) increases, pressure ($ P $) increases linearly.

3. Charles’ Law | 查理定律

For a fixed mass of gas at a constant pressure, its volume is directly proportional to its absolute temperature. 在恆定壓力下，一定質量的氣體，其體積與絕對溫度成正比。

🎈 Formula & Experiment | 公式與實驗

\frac{V_1}{T_1} = \frac{V_2}{T_2}

Experiment Setup: A capillary tube containing a trapped air column (sealed by a drop of concentrated sulfuric acid or oil) is placed in a water bath. (實驗裝置：含有被硫酸滴或油滴封閉的空氣柱的毛細管放入水浴中。)

Heat the water bath. The liquid index moves up as the gas expands. (加熱水浴。氣體膨脹時，液滴會向上移動。)
The pressure remains constant because it is always equal to atmospheric pressure plus the pressure from the liquid index. (壓力保持恆定，因為它始終等於大氣壓力加上液滴產生的壓力。)
Result: As absolute temperature ($ T $) increases, volume ($ V $, proportional to the length of the air column) increases.

4. General Gas Law | 普適氣體定律

By combining Boyle’s, Pressure, and Charles’ Laws, we get the General Gas Law for a fixed mass of gas. 結合波義耳、壓力和查理定律，我們得出一定質量氣體的普適氣體定律。

🌟 The Equations | 方程式

For comparing two states of the same gas: (用於比較同一氣體的兩個狀態：)

\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

The Ideal Gas Equation (using number of moles $ n $ and universal gas constant $ R $): (理想氣體方程：)

$$ P V = n R T $$

⚠️ Crucial Unit Reminders | 單位極度重要！

Many students lose marks because they forget to convert units. Always check these before calculating: (許多學生因為忘記轉換單位而失分。計算前務必檢查：)

Temperature ($ T $): MUST be in Kelvin (K). Never use Celsius!
$T(K) = T(^\circ C) + 273$
Pressure ($ P $): Standard SI unit is Pascal (Pa) or $ N m^{-2} $. (Note: $ 1 \text{ kPa} = 1000 \text{ Pa} $)
Volume ($ V $): Standard SI unit is Cubic Meters ($ m^3 $).
Conversion: $ 1 m^3 = 1000 L = 1,000,000 cm^3 $.

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