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.

OR

The lowest attainable temperature, obtained by plotting the relation between pressure of the gas vs its temperature, where all lines for different gases cut the temperature axis at the same point (−273.15°C), is called the absolute zero of temperature.

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.

OR

The temperature where the solid, liquid, and gas state of a material co-exist in equilibrium, and this occurs only at a unique temperature and pressure, is called the triple point.

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.

The temperature scale where −273.15°C corresponds to 0 K, i.e., the temperature at which the pressure of a gas would become zero, is called the absolute temperature (0 K).

When temperature is constant, the product of pressure and volume of a gas remains constant.

When pressure is constant, the ratio of volume to temperature of a gas remains constant.

When volume is constant, the ratio of pressure to temperature of a gas remains constant.