Question

According to the Sackur–Tetrode formula, the entropy of an ideal monatomic gas grows with the mass of the atoms. Thus the entropy of a volume of argon is much greater than the same volume of helium (at the same T and p). Can you explain this in terms of information entropy?

 

 

Answer 1

Entropy can be defined as the thermodynamic quantity that can be calculated as the ratio of the amount of heat received or liberated to that of the temperature in a reversible process. The Sackur-Tetrode equation is the formula for calculating the entropy of a unit atomic classical ideal gas. The information entropy approach provides the definition of entropy that applies to both physical-based systems and information systems.

 

The expression for the Sackur-tetrode equation is,

 

Here, kB is the Boltzmann constant, m is the gas particle\'s mass, h is the Planck\'s constant, is the number of particles, V is the volume, T is the temperature, Sideal, is the entropy of ideal gas, and U is the internal energy.

 

For an ideal gas, one mole comprises particles in one atomic mass unit at standard temperature and pressure. Entropy increases with molecular weight.

 

The molecular weight of argon and helium are compared. The molecular weight of Argon is 39.940u. The molecular weight of helium is 4.002u. The molecular weight of Argon is higher than that of helium. Molecular weight is required to find out number of grams that are contained in one mole of that chemical component.

 

The fact is that more information is required to correctly represent the intricacies of more intricate systems in a quantitative manner. Information entropy defines the number of bits required to encode the system. Argon has much better information entropy on the basis of information systems possessing a higher log of masses.

 

 The difference of entropy between the different ideal gases at the same temperature and pressure is given by the difference of logarithm of masses. Here, a comparison between the molecular weight of argon and helium is made. So, as the mass of argon is greater than helium, it has higher entropy.

 

Thus, it is proved that the entropy of argon is much greater than that of helium.

Thus, it is proved that the entropy of argon is much greater than that of helium.