The parameters that affect behavior at zero temperature include entropy, internal energy, pressure, volume, and the quantum ground state of a system. This question typically appears in physics and chemistry courses covering thermodynamics, and the answer depends on which specific list of options you’re working from. The core concept, though, is rooted in the Third Law of Thermodynamics and the quantum mechanical properties of matter at absolute zero (0 K, or −273.15 °C).
What Happens at Zero Temperature
Absolute zero is the lowest possible temperature, the point where translational motion of molecules stops in the classical picture. No finite cooling process can actually reach it. But the theoretical limit defines how several thermodynamic parameters behave as temperature approaches zero, and understanding those relationships is what most exam questions are really testing.
The most important parameter is entropy. The Third Law states that the entropy of a pure crystalline substance in its most stable state equals zero at absolute zero. More precisely, the entropy of any system in equilibrium approaches zero as temperature approaches zero, provided the system has a single ground state. If the system has multiple ground states (called degeneracy), entropy at zero temperature equals the Boltzmann constant multiplied by the natural log of the number of those ground states. So the number of ground states directly affects the zero-temperature entropy value.
Parameters That Reach Zero
Entropy is the headline parameter. For a perfect crystal with one unique lowest-energy arrangement, entropy drops to exactly zero at 0 K. This is sometimes called the Nernst heat theorem: the entropy change for any physical or chemical process between condensed phases approaches zero as temperature approaches absolute zero.
Pressure also drops to zero for an ideal gas, since the ideal gas law (PV = nRT) predicts that pressure is directly proportional to temperature. At T = 0, pressure would be zero. In practice, every real gas liquefies or solidifies before reaching absolute zero, so this is a theoretical extrapolation rather than something you’d observe in a lab. Real gases deviate from ideal behavior because their molecules have actual volume and attract each other.
Kinetic energy of particles approaches zero as well. The Boltzmann constant links the average kinetic energy of a particle to the absolute temperature of its surroundings. At 0 K, classical kinetic energy vanishes.
Parameters That Don’t Reach Zero
Volume does not go to zero at absolute zero. Molecules and atoms occupy physical space regardless of temperature. Even though a gas contracts as it cools, the particles themselves have a finite size, and intermolecular forces prevent collapse to zero volume. This is one of the key corrections the van der Waals equation makes to the ideal gas law.
Internal energy also does not reach zero, and this is where quantum mechanics enters the picture. Every quantum system retains a minimum amount of energy even at absolute zero, called zero-point energy. This is the ground state energy of the system, the lowest eigenvalue of its Hamiltonian. It depends on the mass of the particles, the shape of the potential they sit in, and fundamental constants like Planck’s constant. A particle confined in a box or a molecule vibrating around its equilibrium position always has some irreducible energy, no matter how cold it gets.
For systems of fermions (like electrons in a metal), the Fermi energy defines the highest occupied energy level at zero temperature. Electrons fill up available states from the bottom according to the Pauli exclusion principle, with each state holding two electrons of opposite spin. The result is a system with substantial internal energy even at 0 K.
The Key Physical Constants
Several fundamental constants govern how systems behave near absolute zero. The Boltzmann constant (1.381 × 10⁻²³ J/K) sets the scale for thermal energy per particle per degree of temperature. Planck’s constant determines the spacing of quantum energy levels and, by extension, the zero-point energy. The mass of the particles matters too: lighter particles have larger zero-point energy because quantum effects are more pronounced for them.
In Bose-Einstein condensates, the parameters that define the zero-temperature ground state are the atomic mass, the trapping potential, the number of atoms, and the scattering length that characterizes how atoms interact with each other. These inputs fully determine the condensate’s wave function and energy.
Why Absolute Zero Can’t Be Reached
The Third Law has a practical consequence: no finite number of cooling steps can bring a system all the way to 0 K. Each successive cooling step removes less and less entropy, and the process asymptotically approaches but never arrives at absolute zero. A hypothetical engine operating with a zero-temperature cold reservoir would exchange no heat at all, producing no work, which contradicts the framework of thermodynamics itself.
Modern laser cooling techniques can reach about 100 microkelvin, roughly one ten-thousandth of a degree above absolute zero. This requires isolating atoms in a near-perfect vacuum so that stray gas molecules don’t knock them out of their traps. Even at these extreme temperatures, zero-point energy persists, and true absolute zero remains out of reach.
Summary of Affected Parameters
- Entropy: Approaches zero for a perfect crystal with a single ground state.
- Pressure: Approaches zero for an ideal gas (real gases condense first).
- Kinetic energy: Classical translational motion stops at 0 K.
- Internal energy: Does not reach zero due to quantum zero-point energy.
- Volume: Does not reach zero; particles have finite size.
- Ground state degeneracy: Determines whether entropy is exactly zero or a small positive value at 0 K.
If your multiple-choice question lists options like entropy, pressure, volume, and internal energy, the parameters most directly “affected” at zero temperature are entropy (which reaches its minimum value) and pressure (which drops to zero for ideal gases). Volume and internal energy remain nonzero. The exact correct answer depends on how your course frames the question, but the Third Law’s statement about entropy is almost always the central concept being tested.