Suppose that the Gibbs Free Energy of some system is described by the following equation: G(T,P,N)=−NkT...
Suppose that the Gibbs Free Energy of some system is described by the following equation:
G(T,P,N)=−NkT ln ((aT^(5/2))/P)
(a) Find the entropy of this system in terms of T, P, and N.
(b) Find the relationship between V, P, and T for this system. Find one equation relating all of these variables.
(c) Determine the total energy U of this system. Express your
answer as a function of T, P, and N.
Homework Answers
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Suppose that the Gibbs Free Energy of some system is described
by the following equation:
G(T,P,N)=−NkT...
Please explain Gibbs Free Energy. Below are key questions. 1. Define Gibbs free energy and express...
Please explain Gibbs Free Energy. Below are key questions. 1. Define Gibbs free energy and express it mathematically in terms of the temperature, enthalpy change, and entropy change of the system. 2 .Understand the meaning of the mathematical sign of the change in Gibbs free energy with respect to spontaneity. 3 Compute the change in Gibbs free energy, and predict spontaneity from T, DH, and DS.
4. (25 pts) The Gibb's free energy of a system of N particles is given by,...
4. (25 pts) The Gibb's free energy of a system of N particles is given by, G(T,p)=-Nk T In“- (a) dG = ? (write in differential form similar to dU = TDS - pdV) (b) Find expressions for S and V written as partial derivatives with respect to G. (c) Compute the constant pressure heat capacity Cp of the system: C=T(dS/dT), Hint: Use your expression for S derived in (b) above, 3333333 (d) Extract the equation of state for this...
. (40 points) Consider an insulated container of volume V2. N idea gas molecules are initially...
. (40 points) Consider an insulated container of volume V2. N idea gas molecules are initially confined within volume V, by a piston and the remaining volume V2 - Vi is in vacuum. Let T,, P1, E1, S, Al, Hi, G, be the temperature, pressure, energy, entropy, Helmholtz free energy, enthalpy, and Gibbs free energy of the ideal gas at this state, respectively V1 V2-V Using Sackur-Tetrode equation for the entropy of ideal gas where kB R/NA is Boltzmann's constant...
1 The Gibbs Paradox Consider N particles, each of mass m, in a 3-dimensional volume V at temperature T. Each particle i...
1 The Gibbs Paradox Consider N particles, each of mass m, in a 3-dimensional volume V at temperature T. Each particle i has momentum pi. Assume that the particles are non-interacting (ideal gas) and distinguishable. a) (2P) Calculate the canonical partition function N P for the N-particle system. Make sure to work out the integral. b) (2P) Calculate the free energy F--kBTlnZ from the partition function Z. Is F an extensive quantity? c) (2P) Calculate the entropy S F/oT from...
Question 10 Statistical thermodynamics may be used to find the radiation pressure P for cavity (or...
Question 10 Statistical thermodynamics may be used to find the radiation pressure P for cavity (or black body) radiation in terms of the energy per unit volume u. (a) An ideal quantum gas comprises non-interacting identical particles with discrete quantum states labelled 1, 2, ...,r ,....The partition function is given by Z (T,V,N)- > exp(-B(n,&, + п,&, +...)} пп. (i) Define the symbols n1, n2,...,n,...and 81, 82, ..., Er,... (iiExplain why, for photons, the partition function may be expressed as:...
Make a sketch of the Gibbs free energy, G, versus temperature, T, for a single component...
Make a sketch of the Gibbs free energy, G, versus temperature, T, for a single component system as the temperature increases at a fixed pressure, P. Indicate the temperatures where the pure substance changes from liquid to solid, and from solid to gas, and comment on the slopes of the plot of G versus T.
The internal energy, U, is the total energy of a system. For any isolated system, the...
The internal energy, U, is the total energy of a system. For any isolated system, the internal energy is constant. U is a state function, meaning that any path used in calculating AU ill result in the same answer. For any pure substance or fixed mixture of substances, the internal energy, U, can be determined from any two of the variablesP, V, and T. It is often most convenient to choose V and T as the variables. It is helpful,...
3. + 2.5/10 points Previous Answers McM8 6.P.012. The standard Gibbs-free energy of a system is related to its equilibr...
3. + 2.5/10 points Previous Answers McM8 6.P.012. The standard Gibbs-free energy of a system is related to its equilibrium constant through the following equation. AG° = -R·T· In(K) In this equation R is the gas constant, T is the temperature, and the ° next to AG defines the conditions as standard ambient temperature and pressure, i.e. "SATP". (Answer the following questions to three significant figures.) (a) Given an equilibrium constant of 4.53 x 10-6, what is its standard Gibbs-free...
3. Derive the following relationship between the Helmholtz free energy F and the partition function Z for a system of N particles: (a) Starting with the thermodynamic definition F-U-TS, substitute th...
3. Derive the following relationship between the Helmholtz free energy F and the partition function Z for a system of N particles: (a) Starting with the thermodynamic definition F-U-TS, substitute the statistical mechanics results which give U and S in terms of occupation numbers n, state energies e and the most probable number of microstates t* to find, (b) Write out texplicitly in terms of occupation numbers using Stirling's approxima- tion (check the Lagrange multiplier derivation of the Boltzmann distribution)...
I cannot seem to figure it out. The standard Gibbs-free energy of a system is related...
I cannot seem to figure it out.
The standard Gibbs-free energy of a system is related to its equilibrium constant through the following equation. AG = R.T.In(K) In this equation R is the gas constant, T is the temperature, and the next to AG defines the conditions as standard ambient temperature and pressure, i.e. "SATP". (Answer the following questions to three significant figures.) (a) Given an equilibrium constant of 6.28 x 10-3, what is its standard Gibbs-free energy? 4.9 12.6...
4. (25 pts) The Gibb's free energy of a system of N particles is given by, G(T,p)=-Nk T In“- (a) dG = ? (write in differential form similar to dU = TDS - pdV) (b) Find expressions for S and V written as partial derivatives with respect to G. (c) Compute the constant pressure heat capacity Cp of the system: C=T(dS/dT), Hint: Use your expression for S derived in (b) above, 3333333 (d) Extract the equation of state for this...
. (40 points) Consider an insulated container of volume V2. N idea gas molecules are initially confined within volume V, by a piston and the remaining volume V2 - Vi is in vacuum. Let T,, P1, E1, S, Al, Hi, G, be the temperature, pressure, energy, entropy, Helmholtz free energy, enthalpy, and Gibbs free energy of the ideal gas at this state, respectively V1 V2-V Using Sackur-Tetrode equation for the entropy of ideal gas where kB R/NA is Boltzmann's constant...
1 The Gibbs Paradox Consider N particles, each of mass m, in a 3-dimensional volume V at temperature T. Each particle i has momentum pi. Assume that the particles are non-interacting (ideal gas) and distinguishable. a) (2P) Calculate the canonical partition function N P for the N-particle system. Make sure to work out the integral. b) (2P) Calculate the free energy F--kBTlnZ from the partition function Z. Is F an extensive quantity? c) (2P) Calculate the entropy S F/oT from...
Question 10 Statistical thermodynamics may be used to find the radiation pressure P for cavity (or black body) radiation in terms of the energy per unit volume u. (a) An ideal quantum gas comprises non-interacting identical particles with discrete quantum states labelled 1, 2, ...,r ,....The partition function is given by Z (T,V,N)- > exp(-B(n,&, + п,&, +...)} пп. (i) Define the symbols n1, n2,...,n,...and 81, 82, ..., Er,... (iiExplain why, for photons, the partition function may be expressed as:...
The internal energy, U, is the total energy of a system. For any isolated system, the internal energy is constant. U is a state function, meaning that any path used in calculating AU ill result in the same answer. For any pure substance or fixed mixture of substances, the internal energy, U, can be determined from any two of the variablesP, V, and T. It is often most convenient to choose V and T as the variables. It is helpful,...
3. + 2.5/10 points Previous Answers McM8 6.P.012. The standard Gibbs-free energy of a system is related to its equilibrium constant through the following equation. AG° = -R·T· In(K) In this equation R is the gas constant, T is the temperature, and the ° next to AG defines the conditions as standard ambient temperature and pressure, i.e. "SATP". (Answer the following questions to three significant figures.) (a) Given an equilibrium constant of 4.53 x 10-6, what is its standard Gibbs-free...
3. Derive the following relationship between the Helmholtz free energy F and the partition function Z for a system of N particles: (a) Starting with the thermodynamic definition F-U-TS, substitute the statistical mechanics results which give U and S in terms of occupation numbers n, state energies e and the most probable number of microstates t* to find, (b) Write out texplicitly in terms of occupation numbers using Stirling's approxima- tion (check the Lagrange multiplier derivation of the Boltzmann distribution)...
I cannot seem to figure it out.
The standard Gibbs-free energy of a system is related to its equilibrium constant through the following equation. AG = R.T.In(K) In this equation R is the gas constant, T is the temperature, and the next to AG defines the conditions as standard ambient temperature and pressure, i.e. "SATP". (Answer the following questions to three significant figures.) (a) Given an equilibrium constant of 6.28 x 10-3, what is its standard Gibbs-free energy? 4.9 12.6...
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