Question

Why can't temperature go below absolute zero?

Answer 1

1. For N_A (Avogadro's number) molecules of an ideal gas, each having mass m, enclosed in a cubical vessel of volume V and exerting pressure P on the walls of the container, the kinetic gas equation states $PV=\frac{1}{3}m{N}_A{c}^2$ where $c$ is the root mean square velocity of the gas molecules.
2. The Ideal Gas Equation states that for one mole of an ideal gas $PV=RT$ where R is the gas constant and T is the absolute temperature measured in Kelvin.
3. Combining the two equations above, we get $RT=\frac{1}{3}m{N}_A{c}^2$. This equation can be rewritten as

$$\begin{gathered} RT=\frac{2}{3}\times \frac{1}{2}m{N}_A{c}^2 \\ \Rightarrow RT=\frac{2}{3}\times E \\ \Rightarrow E=\frac{3}{2}RT \end{gathered}$$

where $E$ is the translational kinetic energy of the ideal gas molecules.

4. The equation $E=\frac{3}{2}RT$ shows that the kinetic energy and, by extension, the motion of the gas molecules is dependent on the absolute temperature.

5. At absolute zero (0 K), the kinetic energy of the gas molecules is zero i.e. gas molecules stop moving completely at absolute zero. This is why it is not possible to attain a temperature that is below absolute zero.

6. It is not possible to go below absolute zero because the thermal motion of gas molecules ceases at absolute zero.