Absolute Zero and Absolute Temperature

Every gas thermometer in a hospital, every weather balloon, and every rocket engine relies on how gas pressure, volume, and temperature are related. This topic lays the foundation for thermodynamics — and it all starts with defining temperature properly.

The lowest theoretically possible temperature (0 K = −273.15 °C), where ideal gas molecules have zero kinetic energy.

The SI absolute temperature scale starting at absolute zero. Written as K (no degree symbol °).

The unique temperature & pressure at which solid, liquid, and gas phases of a substance coexist in equilibrium.

A hypothetical gas whose molecules have no volume and exert no intermolecular forces; obeys PV = μRT exactly.

A constant in the ideal gas equation; R = 8.31 J mol⁻¹ K⁻¹.

Extending a graph line beyond the measured data to predict values.

One kelvin = 1/273.16 of the difference between absolute zero and the triple point of water.

Master Conversion Formula:

\[\frac {T_C}{100}\] = \[\frac {(T_{F}-32)}{180}\] = \[\frac {(T_{K}-273.15)}{100}\]

Experiments with gases at low densities reveal a simple and powerful pattern:

• At constant pressure: The volume of a gas is directly proportional to its temperature (°C). → Charles' Law
• At constant volume: The pressure of a gas is directly proportional to its temperature (°C). → Gay-Lussac's Law

V ∝ T_C  (at constant P)
P ∝ T_C  (at constant V)

The Graphs Show:

When we plot these relationships, we get straight lines — but with important properties:

• The lines do not pass through the origin (non-zero y-intercept).
• Different gases have different slopes.
• Gases expand linearly with temperature: equal temperature rises cause equal increases in volume (or pressure).

Fig: Volume vs Temperature at Constant Pressure

If we extrapolate the P–T graph backwards — imagining the gas doesn't liquefy — we ask: "At what temperature would the gas pressure drop to zero?"

The answer, from extrapolation, is:

The old two-fixed-point system (ice point + steam point) had a practical problem: the boiling point of water is very sensitive to pressure changes, making calibration difficult. In 1954, scientists adopted a one-fixed-point scale based on the triple point of water.

The triple point is the unique combination of temperature and pressure at which all three phases of a substance — solid, liquid, and gas — coexist in perfect equilibrium.

• The size of one kelvin is identical to one degree Celsius.
• Kelvin is written as K (no degree symbol °). Named after Lord Kelvin (1824–1907).
  T_K = T_C + 273.15

Why Is It Called "Absolute"?

• Based on a universal property of ideal gases, not on any particular substance.
• Its zero point represents the lowest physically possible temperature.
• Unlike the Celsius or Fahrenheit scales, the Kelvin scale has no negative values.

Scale Comparison Table

Three Temperature Scales — Side by Side

"Celsius Adds 273" — To go from Celsius to Kelvin, always add 273.15. To go the other way, subtract. The interval sizes are identical: a change of 1 °C = a change of 1 K.

Building the Equation Step by Step

The ideal gas equation combines two experimental gas laws:

Combining both laws:

\[\frac {PV}{T}\] = constant

For μ moles of any ideal gas, this constant equals μR, giving us:

PV = μRT

The ideal gas equation only works with Kelvin. If the problem gives temperature in Celsius, you must convert to Kelvin first: T(K) = T(°C) + 273.15. Using °C directly will yield an incorrect answer.

• Gases expand linearly with temperature, making them useful for thermometers. This consistent behaviour suggests the existence of a lowest temperature limit.
• Absolute zero (−273.15 °C or 0 K) is the temperature where an ideal gas would have zero pressure. It is the lowest possible temperature.
• The Kelvin scale begins at absolute zero and uses the triple point of water (273.16 K) as a reference point. It is the SI temperature scale.
• The ideal gas equation (PV = μRT) combines all gas laws into a single relationship among pressure, volume, and temperature. It works best for gases at low pressure and high temperature.