GAY-LUSSAC'S LAW

Описание: Gay‑Lussac’s Law is one of the fundamental gas laws that describes the relationship between pressure and temperature of a gas.
Gay‑Lussac’s Law states that:

For a fixed mass of gas at constant volume, the pressure of the gas is directly proportional to its absolute temperature (in Kelvin).

In simpler terms:

If temperature increases, pressure increases
If temperature decreases, pressure decreases

BUT the volume must remain constant.
Mathematical Formula
1. Proportionality Form
P∝TP \propto TP∝T
2. Equation Form
PT=k\frac{P}{T} = kTP​=k
Where:

P = pressure of the gas
T = temperature (in Kelvin)
k = constant

3. Comparison Between Two States
P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}T1​P1​​=T2​P2​​
This is the most commonly used equation in problem-solving.

⚠️ Important: Temperature must be in Kelvin
K=°C+273K = °C + 273K=°C+273

📊 Conceptual Diagram (Text Form)
Constant Volume Container:
Temperature ↑ → Molecules move faster → Collisions ↑ → Pressure ↑
Temperature ↓ → Molecules move slower → Collisions ↓ → Pressure ↓


🔬 Why This Happens — The Physics Behind It
When temperature increases:

Gas molecules gain kinetic energy.
They move faster and collide more frequently and forcefully with the container walls.
Collisions create pressure.
Since the container volume cannot change, pressure must increase.


🧪 Example Problem
Given:
A gas has a pressure of 2 atm at 300 K.
What is the pressure at 450 K?
Solution:
P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}T1​P1​​=T2​P2​​
2300=P2450\frac{2}{300} = \frac{P_2}{450}3002​=450P2​​
Cross multiply:
P2=2×450300P_2 = \frac{2 \times 450}{300}P2​=3002×450​
P2=3 atmP_2 = 3 \text{ atm}P2​=3 atm
📌 Pressure increased because temperature increased.

📝 Conditions for Gay‑Lussac’s Law to Apply


Volume must be constant
(Rigid, sealed container)


Gas amount must be constant
(No leaks)


Temperature must be in Kelvin


Gas behaves ideally
(Assumption for simplicity)



🚗 Real-Life Applications
⭐ 1. Pressure Cooker

As temperature inside increases
Pressure rises
Food cooks faster
Gay‑Lussac’s Law in action.

⭐ 2. Car Tires

On hot days, tire pressure increases.
On cold days, pressure decreases.

⭐ 3. Aerosol Cans

Heating increases pressure dangerously.
Warning labels advise against exposing to heat.

⭐ 4. Scuba Tanks

Tanks heat during filling → pressure rises.
Must cool and repressurize for accuracy.

⭐ 5. Fire Sprinkler Systems

High heat increases gas pressure in pipes
→ activates sprinklers.


🔄 Relationship to Other Gas Laws























Gas LawVariables RelatedConstantBoyle's LawP ∝ 1/VT constantCharles's LawV ∝ TP constantGay-Lussac’s LawP ∝ TV constantCombined Gas LawP, V, TAmount constant
Gay-Lussac’s Law is part of the Combined Gas Law.

🧠 Quick Summary (Easy to Memorize)
Gay-Lussac's Law: Pressure ↗ when Temperature ↗ (Volume stays constant)
Formula:
P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}T1​P1​​=T2​P2​​
Applications: Tires, pressure cookers, aerosol cans, scuba tanks.

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