Finding a Helmholtz free energy from the equation of state

Alexander Lewis
2022-10-22
Answered

Finding a Helmholtz free energy from the equation of state

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Momellaxi

Answered 2022-10-23
Author has **14** answers

The Helmholtz free energy per particle $f=F/N$, is related to the pressure P by the relation:

$P={\rho}^{2}{\frac{\mathrm{\partial}f}{\mathrm{\partial}\rho}|}_{T}$

Since the partial derivative is taken at constant T, it could be integrated only within an unknown function of T

Additional information, like the specific heat, has to be used in order to find the full $\rho $ and T dependence.

$P={\rho}^{2}{\frac{\mathrm{\partial}f}{\mathrm{\partial}\rho}|}_{T}$

Since the partial derivative is taken at constant T, it could be integrated only within an unknown function of T

Additional information, like the specific heat, has to be used in order to find the full $\rho $ and T dependence.

asked 2022-09-06

Can we prove that the thermodynamic state of a system is completely determined by any two out of the three factors P,V and T ?

asked 2022-08-20

Suppose a particle with a definite energy is going in empty space from a location ${\mathit{r}}_{\mathbf{1}}$ to a location ${\mathit{r}}_{\mathbf{2}}$. In other words, it is a free particle with no forces on it. Except for a numerical factor in front, the amplitude to go from ${\mathit{r}}_{\mathbf{1}}$ to ${\mathit{r}}_{\mathbf{2}}$ is

$\begin{array}{}\text{(3.7)}& \u27e8{\mathit{r}}_{\mathbf{2}}|{\mathit{r}}_{\mathbf{1}}\u27e9=\frac{{e}^{\frac{i}{\hslash}p{r}_{12}}}{{r}_{12}}.\end{array}$

$\begin{array}{}\text{(3.7)}& \u27e8{\mathit{r}}_{\mathbf{2}}|{\mathit{r}}_{\mathbf{1}}\u27e9=\frac{{e}^{\frac{i}{\hslash}p{r}_{12}}}{{r}_{12}}.\end{array}$

asked 2022-05-10

Why might you expect the canonical partition function to scale exponentially with the system size, thus always ensuring that the Helmholtz free energy is extensive?

asked 2022-11-04

Why is Gibbs free energy not used in Statistical Associating Fluid Theory (SAFT) Equation of State (EoS)?

asked 2022-05-14

(a) Which of the following corresponds to additional non-expansion work?

- Entropy

- Helmholtz energy

- Enthalpy

- Gibbs energy

(b) What is the basis for deriving an expression for entropy as a function of temperature and volume?

- Helmholtz energy

- Gibbs energy

- Internal energy

- Enthalpy

- Entropy

- Helmholtz energy

- Enthalpy

- Gibbs energy

(b) What is the basis for deriving an expression for entropy as a function of temperature and volume?

- Helmholtz energy

- Gibbs energy

- Internal energy

- Enthalpy

asked 2022-08-19

When we try to find the heat capacity which will be used to calculate the inner energy, it would not be very hard when neglecting the force interactions between atoms, such as ideal gas. But if we consider the interactions, is it possible to find out the expression of Helmholtz free energy from the EOS?

asked 2022-04-06

Calculate delta G and delta A for the freezing of 1.00 mol of H2O at 0oC and 1 atm. The heat of fusion of water at 0oC is 6002 J mol-1. The density of ice at 0oC and 1 atm is 0.917 g cm-3, and that of water at the same conditions is 1.000 g cm-3.

The correct answers are 0; -0.16 respectively but i'm getting a different one

The correct answers are 0; -0.16 respectively but i'm getting a different one