At what temperature does entropy become zero and entropy decrease with temperature increase?
The Third Law of thermodynamics that the entropy of a perfect crystal of a pure component at 0 K is zero.
An entropy decrease with increasing temperature means a negative heat capacity [(dS/dT)V = CV/T] or a negative temperature. Such a system would be thermodynamically unstable, i.e., it cannot be in an equilibrium state.
You could try considering the entropy calculation in the NVT ensemble, i.e.
S=klnQ+kT(dlnQ/dT)
Q(N,V,T)=sum_i(exp(-E_i/kT)), the partition function in the NVT ensemble
E_i is the energy of state "i", k is the Boltzmann constant, and T is the absolute temperature. T>=0
According to the equations presented by Y. Mauricio Muñoz-Muñoz a system with a population inversion may be formally regarded as being at a negative temperature. An example is a solid-state laser in operation, where there is an electronically excited niveau artificially populated. This can be characterized with a negative electronic temperature. At the same time, the vibrations in the laser medium are thermally distributed with a positive temperature. Evidently, such a system is an open system, and not in thermal equilibrium.
I agree with Ulrich Deiters that at absolute zero the system must be in a state with the minimum possible energy. Entropy is related to the number of accessible microstates, and there is typically one unique state with minimum energy. In such a case, the entropy at absolute zero will be exactly zero. The third law of thermodynamics states that the entropy of a perfect crystal at a temperature of zero Kelvin is equal to zero. At absolute zero of temperature, there is complete orderly molecular arrangement in the crystalline substance. Therefore, there is no randomness at 0 K and entropy is taken to be zero. In a chemical reaction, when we increase temperature of any substance, molecular motion increase and so does entropy. Conversely, if the temperature of a substance is lowered, molecular motion decrease, and entropy should decreases. Entropy generally increases when a reaction produces more molecules than it started with. Entropy generally decreases when a reaction produces fewer molecules than it started with. If there is no difference in the final and initial state of entropy then entropy will be zero. Devices with a steady state of flow of energy like nozzles, and turbines have zero entropy. Reversible processes also have zero entropy.
Hello,
two suggestions:
(i) In long range systems (e.g. in astrophysics) negative heat capacity appears. In these cases you should look to local equilibrium (local max for entropy). These systems do not contradict the second law.
(ii) at T=0K all degrees of freedom are frozen (classical), so the entropy should approach zero.
At absolute 0 kelvin entropy becomes 0 according to third law. For binary system of 2 energy states there is a possibility of decrease in entropy for states where no of particles occupying higher energy level becomes more than the particles in lower energy state.
Anuradha Gupta's comment pertains to the population inversion in lasers. There one can indeed have an unusual behaviour of the entropy – but only for one degree of freedom, e.g., electronic excitation. On the whole, however, lasers are not in a thermodynamically stable state.
M. A. Amato's remark pertains to black holes. These must be considered unstable and not in thermodynamic equilibrium. Black holes (should) decay by emitting Hawking radiation. Massive black holes, however, may take many billions of years.
- Badges
- Science topic