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GAY-LUSSAC'S LAW

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. 🎙️ New to streaming or looking to level up? Check out StreamYard and get $10 discount! 😍 https://streamyard.com/pal/d/59840512...