Table of Contents
Temperature from the Ideal Gas Law
Temperature in the context of the ideal gas law is an absolute measure of the average kinetic energy of gas molecules. By measuring the pressure, volume, and amount of a gas, we can determine its temperature using the rearranged ideal gas equation. This is the basis of gas thermometry, one of the most fundamental methods for establishing temperature standards.
The temperature must always be expressed in Kelvin for the ideal gas law to work correctly. Zero Kelvin (absolute zero, -273.15 degrees C) represents the theoretical state where molecular motion ceases entirely. No real system has ever reached exactly 0 K, though laboratory experiments have come within billionths of a degree.
The Formula
Where T is temperature in Kelvin, P is pressure in atm, V is volume in liters, n is moles, and R = 0.08206 L·atm/(mol·K).
Temperature Scale Conversions
| Reference Point | Kelvin | Celsius | Fahrenheit |
|---|---|---|---|
| Absolute Zero | 0 K | -273.15 °C | -459.67 °F |
| Water Freezes | 273.15 K | 0 °C | 32 °F |
| Room Temperature | 293.15 K | 20 °C | 68 °F |
| Water Boils | 373.15 K | 100 °C | 212 °F |
Kinetic Energy Connection
The average translational kinetic energy of an ideal gas molecule is directly proportional to the absolute temperature:
Where k is Boltzmann's constant (1.381 x 10^-23 J/K). This means temperature is fundamentally a measure of molecular motion. At higher temperatures, molecules move faster and collide harder, producing higher pressure.
Frequently Asked Questions
Why can't temperature be negative in Kelvin?
The Kelvin scale starts at absolute zero, where molecules have minimum possible energy (zero-point energy in quantum mechanics). Since kinetic energy cannot be negative, and temperature is directly proportional to average kinetic energy, temperature in Kelvin is always non-negative.
What is STP and SATP?
STP (Standard Temperature and Pressure) is 0 degrees C (273.15 K) and 1 atm (101.325 kPa). SATP (Standard Ambient Temperature and Pressure) is 25 degrees C (298.15 K) and 1 bar (100 kPa). SATP is the newer IUPAC standard and gives a molar volume of 24.79 L rather than 22.41 L at STP.