Gay-Lussac's Law, discovered by French chemist Joseph Louis Gay-Lussac in 1802, states that at constant volume, the pressure of a gas is directly proportional to its absolute temperature. This relationship can be expressed mathematically as P is proportional to T, or in equation form as P1 over T1 equals P2 over T2. When we heat gas molecules in a fixed container, they move faster and collide with walls more frequently, increasing pressure.
The kinetic molecular theory provides the molecular basis for Gay-Lussac's Law. When temperature increases, gas molecules move faster due to increased kinetic energy. These faster-moving molecules collide with the container walls more frequently and with greater force. Since the container volume remains constant, this increased molecular activity results in higher pressure. The average kinetic energy is directly proportional to absolute temperature, as shown by the equation KE average equals three-halves k T.
The mathematical derivation of Gay-Lussac's Law starts with the direct proportionality between pressure and temperature. This gives us P equals k T, where k is a constant. For two different states of the same gas, we get P1 over T1 equals P2 over T2. The graph shows this linear relationship, with pressure on the y-axis and absolute temperature on the x-axis. Notice the line passes through absolute zero, emphasizing that temperature must be in Kelvin, not Celsius. Remember to convert Celsius to Kelvin by adding 273.15.
Gay-Lussac's Law has many practical applications in daily life. Car tire pressure increases in summer due to higher temperatures, which is why you should check tire pressure when tires are cool. Pressure cookers use this principle - high temperature creates high pressure, allowing food to cook faster. Aerosol cans have temperature warnings because heating them can cause dangerous pressure buildup and potential explosion. Weather balloons also demonstrate this law as they experience pressure changes with temperature variations at different altitudes.
Let's solve a typical Gay-Lussac's Law problem. A gas at 27 degrees Celsius has a pressure of 2 atmospheres. What will be the pressure at 127 degrees Celsius? First, convert temperatures to Kelvin: 300 K and 400 K. Using the formula P2 equals P1 times T2 over T1, we get P2 equals 2 times 400 over 300, which equals 2.67 atmospheres. Remember, Gay-Lussac's Law has limitations - it only applies to ideal gases and breaks down at very high pressures or very low temperatures. It connects with other gas laws to form the combined gas law.