Question

The Helmholtz free energy of a system is given by A = U - TS. Give a graphical illustration of the criterion for equilibrium of a closed solid-vapour system at constant volume and temperature by using this equation

Answer #1

Starting with the definition of Helmholtz Energy
A=U-TS
prove that the change in Helmholtz Energy for a process at
constant temperature is the total work (expansion and non-expansion
work).

Use the master equation for Helmholtz free energy, A,
to determine the change in entropy as a function of volume under
constant temperature conditions (ds/dv) for a van der waals gas

Using the machinery of statistical mechanics calculate the
internal energy (U), the function of
Helmholtz (F), Gibbs free energy (G), enthalpy (H) and specific
heat of a
quantum harmonic oscillator.

There is a hypothetic system of N particles, there internal
energy is given by U(S,L,n) = θ(S^2)V/(N^2)
where θ is a constant and V is the volume of the system and S is
the entropy of the system. Assume the system is under the
equilibrium.
i) Show U(S,L,n) is a ﬁrst order Euler function.
ii) Calculate the chemical potential µ(S,L,N)
iii) Calculate the chemical potential µ(L/N)
iv) Show the equation of state satisﬁes the Gibbs-Duhem relation
below SdT + VdP...

Give a specific example of a system with the energy
transformation U-->delta Eth (U and Eth are the potential and
the thermal energies of the system) Any energy not mentioned in the
transformation is assumed to remain constant; if work is not
mentioned it is assumed to be zero.

The system decreased its volume by 3L, at constant pressure p=3bar
and constant temperature. The resulting change in Helmholtz free
energy is (in kJ)

± Free Energy and Chemical Equilibrium
The equilibrium constant of a system, K, can be related
to the standard free energy change, ΔG, using the
following equation:
ΔG∘=−RTlnK
where T is standard temperature in kelvins and
R is equal to 8.314 J/(K⋅mol).
Under conditions other than standard state, the following
equation applies:
ΔG=ΔG∘+RTlnQ
In this equation, Q is the reaction quotient and is
defined the same manner as K except that the
concentrations or pressures used are not necessarily the...

The equilibrium constant of a system, K, can be related
to the standard free energy change, ΔG∘, using the
following equation:
ΔG∘=−RTlnK
where T is a specified temperature in kelvins (usually
298 K) and R is equal to 8.314 J/(K⋅mol).
Under conditions other than standard state, the following
equation applies:
ΔG=ΔG∘+RTlnQ
In this equation, Q is the reaction quotient and is
defined the same manner as K except that the
concentrations or pressures used are not necessarily the
equilibrium values....

The equilibrium constant of a system, K, can be related
to the standard free energy change, ΔG∘, using the
following equation:
ΔG∘=−RTlnK
where T is a specified temperature in kelvins (usually
298 K) and R is equal to 8.314 J/(K⋅mol).
Under conditions other than standard state, the following
equation applies:
ΔG=ΔG∘+RTlnQ
In this equation, Q is the reaction quotient and is
defined the same manner as K except that the
concentrations or pressures used are not necessarily the
equilibrium values....

± Gibbs Free Energy: Temperature Dependence Gibbs free energy
(G) is a measure of the spontaneity of a chemical reaction. It is
the chemical potential for a reaction, and is minimized at
equilibrium. It is defined as G=H−TS where H is enthalpy, T is
temperature, and S is entropy.
The chemical reaction that causes aluminum to corrode in air is
given by
4Al+3O2→2Al2O3
in which at 298 K
ΔH∘rxn
= −3352 kJ
ΔS∘rxn
= −625.1 J/K
Part A
What is...

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