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The gas laws

Boyle's lawCharles's lawcombined gas lawideal gas law

Boyle, Charles, Gay-Lussac, the combined law and the ideal gas law — each holding one property fixed, and how they collapse into PV = nRT.

Boyle's Law

P1V1=P2V2P_1 V_1 = P_2 V_2

At constant temperature, pressure times volume stays constant for a fixed amount of gas.

Charles's Law

V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}

At constant pressure, gas volume is directly proportional to absolute temperature.

Gay-Lussac's Law

P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}

At constant volume, gas pressure is directly proportional to absolute temperature.

Combined Gas Law

P1V1T1=P2V2T2\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

For a fixed amount of gas, pressure times volume over absolute temperature stays constant between any two states.

Ideal Gas Law

PV=nRTP V = n R T

Relates pressure, volume, amount, and temperature of a gas. R = 8.314 J/(mol·K).

How they fit together

Each of the first three holds one thing constant and watches two others trade off: Boyle fixes temperature (P and V trade), Charles fixes pressure (V and T rise together), Gay-Lussac fixes volume (P and T rise together). The combined law is simply all three at once for a fixed amount of gas, and the ideal gas law is the combined law with the amount allowed to change too, which is what the n and the R buy you.

The universal trap is temperature. Every one of these needs absolute temperature: doubling from 20 °C to 40 °C is a rise of about 7%, not 100%, because it is 293 K to 313 K. Solve one of these in Celsius and the answer is not slightly wrong, it is meaningless.