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2. (25 pts) Derive the (a) Maxwell relation for the Helmholtz Free Energy F=U-TS. Show ALL...
Derive the Maxwell equations for F (Helmholtz Free Energy) and G (Gibbs Free Energy) with “for all mathematical stages&#...
Derive the Maxwell equations for F (Helmholtz Free Energy) and G (Gibbs Free Energy) with “for all mathematical stages"? What is the condition of being a state function, and which of the parameters E (Internal energy), Q (Heat), W (Work), S (Entropy) are not the state function? Why is that?
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)...
physical chemistry 3. Derive formulas for AE, Aw, and Aq when a Van der Waal's gas...
physical chemistry
3. Derive formulas for AE, Aw, and Aq when a Van der Waal's gas undergoes: a) reversible isothermal expansion b) adiabatic expansion c) repeat steps a and b for an ideal gas d) Use the Maxwell relation derived from the Helmholtz free energy F =F(T,V) = -SdT PdV To prove that e) Determine for a Van der Waal's gas and an ideal gas. T()-P f) Explain the answer to part e in terms of the assumptions that define...
5. (a) Derive the following Maxwell relation for a fluid system: ()-), (b) Show that for...
5. (a) Derive the following Maxwell relation for a fluid system: ()-), (b) Show that for an ideal gas at a given temperature T, the chemical potential difference between an arbitrary pressure, P, and a reference pressure, Po, is given by u(P) – u(Po) = kbT In (P/Po). (c) For the case of an incompressible liquid, the volume per particle, v = V/N, is independent of the pressure; show that in this case, one has u(P) – ”(Po) = v...
2. Consider free expansion of a gas when the internal energy U remains constant. Derive: a) the e...
2. Consider free expansion of a gas when the internal energy U remains constant. Derive: a) the expression for (дт/avJu in terms of P, T, Cv and (ap/aT)v b) the expression for (as/aV)u in terms of P and T c) using equations obtained in a) and b) calculate (expression for) the change of temperature AT and change of entropy AS for a free gas expansion from Vi to V2.
2. Consider free expansion of a gas when the internal energy...
Please show all work, thank you. μ,NIR 2(R2 +x) 2. (50 pts) The expression for the...
Please show all work, thank you.
μ,NIR 2(R2 +x) 2. (50 pts) The expression for the magnetic field on the axis of a current loop is B,(x) A Helmholtz coil is comprised of two identical coils separated by the distance R, with one coil at the origin and the other shifted over at Xo = R (the radius of the coils), where the current runs counterclockwise in both. It is a useful tool because the magnetic field at the center...
You are working for a venture capital firm and are tasked with determining if an invention...
You are working for a venture capital firm and are tasked with determining if an invention should be considered for financial feasibility studies. The invention consists of a tube into which compressed air is admitted. The tube separates the compressed air at an intermediate temperature into two air flows, one hot and one cold. A schematic of the invention is shown below in fig. 1. The compressed air admitted into the device is divided such that 60% of it exits...
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)...
physical chemistry
3. Derive formulas for AE, Aw, and Aq when a Van der Waal's gas undergoes: a) reversible isothermal expansion b) adiabatic expansion c) repeat steps a and b for an ideal gas d) Use the Maxwell relation derived from the Helmholtz free energy F =F(T,V) = -SdT PdV To prove that e) Determine for a Van der Waal's gas and an ideal gas. T()-P f) Explain the answer to part e in terms of the assumptions that define...
5. (a) Derive the following Maxwell relation for a fluid system: ()-), (b) Show that for an ideal gas at a given temperature T, the chemical potential difference between an arbitrary pressure, P, and a reference pressure, Po, is given by u(P) – u(Po) = kbT In (P/Po). (c) For the case of an incompressible liquid, the volume per particle, v = V/N, is independent of the pressure; show that in this case, one has u(P) – ”(Po) = v...
2. Consider free expansion of a gas when the internal energy U remains constant. Derive: a) the expression for (дт/avJu in terms of P, T, Cv and (ap/aT)v b) the expression for (as/aV)u in terms of P and T c) using equations obtained in a) and b) calculate (expression for) the change of temperature AT and change of entropy AS for a free gas expansion from Vi to V2.
2. Consider free expansion of a gas when the internal energy...
Please show all work, thank you.
μ,NIR 2(R2 +x) 2. (50 pts) The expression for the magnetic field on the axis of a current loop is B,(x) A Helmholtz coil is comprised of two identical coils separated by the distance R, with one coil at the origin and the other shifted over at Xo = R (the radius of the coils), where the current runs counterclockwise in both. It is a useful tool because the magnetic field at the center...
You are working for a venture capital firm and are tasked with determining if an invention should be considered for financial feasibility studies. The invention consists of a tube into which compressed air is admitted. The tube separates the compressed air at an intermediate temperature into two air flows, one hot and one cold. A schematic of the invention is shown below in fig. 1. The compressed air admitted into the device is divided such that 60% of it exits...
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