### Question

Is the 3rd law of thermodynamics valid even for objects smaller than atoms?

Asked by:
Annelie Damberg

### Answer

Yes the third law of thermodynamics holds for any system - classical or quantum mechanical.
It basically states that absolute zero (0K or -273.16°C) cannot be reached and that its entropy is zero. Entropy is the number of possible arrangements of a system - so a zero entropy means that no possible states can exist at absolute zero. But lets think about why. Temperature is a measure of the internal energy of a system - which contains both kinetic and potential energy. It is easier to simply consider the kinetic energy (this is basically taking the ideal gas model of kinetic theory). At absolute zero the internal energy of the system would be zero since temperature is proportional to internal energy. This means that all particles in the system would be completely at rest in their positions. But this means that they will have a definite position and a definite momentum (ie zero). This violates Heisenberg's Uncertainty Principle which states that the product of uncertainty in position and momentum must always be greater than Planck's constant divided by two pi. So that is why the third law of thermodynamics holds for everything.

Answered by:
Martin Archer, Physics Student, Imperial College, London, UK