Pressure, Temperature, and the Kelvin Scale

From the previous topic, pressure comes from gas particles colliding with the walls of their container. Each collision delivers a tiny force over a tiny area; pressure is defined as force per unit area, $P=F/A$. More particle collisions per second, or harder collisions (higher speed), both increase pressure. This is why heating a gas at constant volume increases its pressure — the particles move faster and hit the walls harder and more often.

The air around you is also a gas pressing on everything it touches. In 1643 Evangelista Torricelli filled a glass tube with mercury, turned it upside down in a dish of mercury, and found that the column always dropped to about 760 mm tall at sea level. The empty space above the mercury holds essentially no gas, so the only thing holding the column up is the atmosphere pushing down on the mercury in the dish. That is where the unit millimetres of mercury comes from, and it is why a barometer measures air pressure by the height of a liquid column. Mercury is used because it is very dense (about 13.6 g/mL): a water barometer would need a column about 10.3 m tall. Air pressure falls as you climb, because there is less air above you pushing down. At the summit of Mount Everest it is only about one-third of sea-level pressure, which is also why water boils there at roughly 70°C instead of 100°C.

Pressure shows up in several different units depending on context (weather reports, chemistry labs, engineering). You need to be able to convert freely between them. The SI unit is the pascal ($1\text{Pa}=1{\text{N/m}}^2$), which is tiny: one pascal is roughly the pressure a sheet of paper exerts resting on a table. That is why chemists use kilopascals ($1\text{kPa}=1000\text{Pa}$); normal air pressure is about 101 kPa, and Canadian weather reports give it in kPa. The standard atmosphere (atm) was defined as the average sea-level pressure, which is why 1 atm lands on the awkward-looking 101.325 kPa. The SATP standard uses a rounder 100 kPa (also called 1 bar).

This is the single most important conceptual point in the whole unit. Every gas law relates gas properties using ratios or direct proportions with temperature. Those relationships only work if temperature is measured on a scale where zero actually means zero — that is, zero average kinetic energy, with no negative values possible. The Celsius scale's zero point (0°C, the freezing point of water) is completely arbitrary; it has nothing to do with particle motion. The Kelvin scale fixes this: 0 K ("absolute zero") is the temperature at which particle motion is theoretically at a minimum, and the Kelvin scale has no negative values.

• Always convert given temperatures to Kelvin BEFORE plugging into any gas law equation.
• Temperature differences ($\Delta T$) are numerically the same in °C and K (a 10°C change is also a 10 K change) — but absolute temperatures ($T$ itself) are NOT interchangeable between the scales.
• A negative Kelvin temperature is physically impossible; if your answer comes out negative, you've made an error.
• Kelvin temperatures are written without a degree sign: 298 K, not 298°K. One kelvin is the same size step as one Celsius degree; only the starting point differs.
• Absolute zero is $0\text{K}=-273.15$°C. It can be approached (labs have reached a tiny fraction of a kelvin above it) but never quite reached.
• Which unit to use: if a problem will use $PV=nRT$ with $R=8.314$, convert every pressure to kPa first. For ratio laws (Boyle, Charles, combined), any pressure unit works as long as both pressures match, but temperature must ALWAYS be in kelvins.