# 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 h^{2}))^{(3/2)}.

For the ideal gas the entropy is,

S=N k(Log(Ω )+5/2)

Having 10^{19} particles of mass 1 gr, with an energy U=500 J, in a volume of 1 m^{3}, what is the entropy the system?

Answer:

Substituting in Ω the values:

Ω = 1 m^{3}/10^{19} ((4 * π * 0.001 Kg * 500 J)/(3 * 10^{19} * (6.62*10^{(-34)}m^{2} Kg/s)^{2}))^{(2/3)}

Ω = 3.3*10^{(58)}

then,

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

S = 0.17 J/K

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