Entropy Formula

Entropy is a measure how much the energy of atoms and molecules become more spread out in a process and can be defined in terms of statistical probabilities of a system or in terms of the other thermodynamic quantities. The most familiar case is the entropy of an ideal gas.

Entropy = (Boltzmann constant) * logarithm (number of possible states of the system)

The equation is:

S= k Log(Ω)

Where:

S: Entropy

k: Boltzmann constant. (1.38*10^(-23) J/ K)

Ω: The number of states of the system.

Thermodynamic work Formula Question:

1) If an ideal gas is in a box full, the number of states possible are given by

Ω = V/N((4 π m U)/(3 N h²))^(3/2).

For the ideal gas the entropy is,

S=N k(Log(Ω )+5/2)

Having 10¹⁹ particles of mass 1 gr, with an energy U=500 J, in a volume of 1 m³, what is the entropy the system?

Answer:

Substituting in Ω the values:

Ω = 1 m³/10¹⁹ ((4 * π * 0.001 Kg * 500 J)/(3 * 10¹⁹ * (6.62*10^(-34)m² Kg/s)²))^(2/3)

Ω = 3.3*10⁽⁵⁸⁾

then,

S = 10¹⁰ * (1.38*10^(-23)J/K)*(Log(3.3*10⁽⁵⁸⁾) + 5/2)

S = 0.17 J/K