Lei Combinada dos Gases

Combined gas law: P₁V₁/T₁ = P₂V₂/T₂

The combined gas law rolls Boyle's, Charles's and Gay-Lussac's laws into one relation. It covers a fixed amount of ideal gas whose pressure, volume and temperature all shift at once: PV/T = constant. Two conditions matter. Temperature has to be in Kelvin, and the amount of gas in moles stays put, so no leaks and no reactions. For instance, take 10 L at 1 atm and 273 K and compress it to 2 atm and 546 K. Then V₂ = (1·10·546)/(2·273) = 10 L. Hold one variable steady and it falls back to the simpler laws: Boyle's when T₁ = T₂, Charles's when P₁ = P₂, Gay-Lussac's when V₁ = V₂.

Applications

It predicts how a weather balloon swells as pressure and temperature drop with altitude. Engineers use it to design industrial gas-handling systems and to size HVAC duct flow. Divers care about it too: gases compress at depth and warm or cool with their surroundings, which has direct safety implications for scuba and free-diving. And it's a staple of high-school and entrance-exam problems.

FAQ

What if the number of moles changes? Switch to the full ideal gas law, PV = nRT. The combined law only holds while n stays constant.

Can I use Celsius? No. Convert to Kelvin first (K = °C + 273.15). Celsius produces wrong answers, and the error gets ugly near or below 0 °C.

How accurate is it for real gases? Very good at moderate pressures and at temperatures well above the gas's boiling point. Once you get near condensation or push past about 10 atm, reach for van der Waals or bring in the compressibility factor Z.