# What is the Sackur-Tetrode expression for the entropy of a monatomic ideal gas?

• S_Flaherty
In summary, the Sackur-Tetrode expression for the entropy of a monatomic ideal gas is S = Nk[ln(V/N(4πmK^3T^3/P^2h^3)^(3/2)) + 5/2]. This was found using the equations PV = NkT and U = (3/2)NkT, with a correction for the number of degrees of freedom (f = 3). It is always a good idea to double check your work for mistakes before moving on to the next part of a problem.
S_Flaherty

## Homework Statement

Write the Sackur-Tetrode expression for the entropy of a monatomic ideal gas as a function of pressure, temperature, and number, S(N,T,P).

## Homework Equations

S = Nk[ln(V/N(4πmU/3Nh2)3/2) + 5/2]
PV = NkT
U = (f/2)NkT

## The Attempt at a Solution

I found that equation for S in my book and also found that f = 3 for monatomic gases. So I used V = NkT/P and U = (3/2)NkT and just put it into the equation for S to get:
S = Nk[ln(KT/P(2πmT/h2)3/2) + 5/2].

I just wanted to see if I got this right because sometimes I make stupid mistakes and I didn't want to continue to the next part of the problem if got this part incorrect.

Hello.

Looks pretty good, but I don't think you have enough factors of K in your expression. Also, you might want to combine all factors of K and T to make it look a little nicer.

## 1. What is Sackur-Tetrode expression?

Sackur-Tetrode expression is a mathematical equation used to calculate the entropy of a gas or a collection of particles at a given temperature and volume. It was developed by German physicist Hugo Sackur and Russian physicist Yakov Fyodorovich Tetrode in the early 20th century.

## 2. How is Sackur-Tetrode expression derived?

Sackur-Tetrode expression is derived using statistical mechanics principles, specifically the Boltzmann entropy formula and the ideal gas law. It takes into account the number of particles, the volume, and the temperature of the gas to calculate its entropy.

## 3. What is the significance of Sackur-Tetrode expression?

Sackur-Tetrode expression is significant because it provides a way to calculate the entropy of a gas or a collection of particles, which is a measure of the disorder or randomness of a system. It also helps in understanding and predicting the behavior of gases at different temperatures and volumes.

## 4. Can Sackur-Tetrode expression be applied to all gases?

No, Sackur-Tetrode expression is most accurate for monatomic gases (such as helium, neon, and argon) at low to moderate pressures. It can also be applied to diatomic gases (such as oxygen and nitrogen) with some adjustments, but it may not be as accurate for more complex molecules.

## 5. How is Sackur-Tetrode expression used in practical applications?

Sackur-Tetrode expression is commonly used in thermodynamics and statistical mechanics to calculate the entropy of gases in various physical and chemical processes. It is also used in fields such as astrophysics and atmospheric science to study the behavior of gases in different environments.

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