A=U-TS is Helmholtz free energy, which is commonly used in statistical thermodynamics. Starting from dU=TdS-pdV, show that dA=-SdT-pdV
A=U-TS is Helmholtz free energy, which is commonly used in statistical thermodynamics. Starting from dU=TdS-pdV, show...
Problem 2 dH-d(U + PV) = dU + PdV +Vdp = TdS +Vdp ㈜,-을 and㈜T,I㈜rl Pr ove that: Starting from: dH- and Problem 2 dH-d(U + PV) = dU + PdV +Vdp = TdS +Vdp ㈜,-을 and㈜T,I㈜rl Pr ove that: Starting from: dH- and
1. Starting with the definition of the Helmholtz Energy: A U-TS , determine an expression for AA is under constant (a) isothermal or (b) isoentropic conditions. 2. Starting with the definition of the Gibbs Free Energy: G-H-TS determine an expression for AG is under constant (a) isothermal or (b) isoentropic conditions.
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)...
2. (25 pts) Derive the (a) Maxwell relation for the Helmholtz Free Energy F=U-TS. Show ALL steps and justifications in your derivation. Using your result in (a) comment on how (b) the entropy behaves for an isothermal expansion of an ideal gas. Finally, show the validity of the following equations (c) U = F-TOOF) -T2 and at (T) 01 (d) C =-1(
(b) We would like to demonstrate that the appropriate free energy is minimized in thermodynamic equilibrium by considering a system at constant temperature and pressure, for which the Gibbs free energy G-U-TS+ PV is appropriate o Write down the first law of thermodynamics linking heat, q, to AU and work Au-grw i) du tfestdv ) du dsreu Tds-Pdv-) sPdV dus Write down an inequality relating the temperature-weighted entropy change, TAS to q ds ii) Use the result of (i) and...
Thermodynamics Show that the reduced chemical potential and the reduced Helmholtz free energy for a Van der Waals gas in terms of the reduced variables and can be written as: and graph parametrically vs for fixed values (pec (pec We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image3T6 Biu Biu RT μ (w) π (w) We were unable to transcribe this image (pec (pec 3T6 Biu Biu RT μ (w)...
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:...
10. Given the following table: Compound NO: (g) N:O (g) AHP (J mol) AGP (J mol) 51.84 33.85 9.66 98.29 For the reaction: N:Oa (g) eo 2NO: (g) (a) Use the information in the Table to calculate AG for the reaction (b) Use the information in the Table to calculate AH" for the reaction (c) Calculate K, at 25 C. (d) Calculate K, at 1600 °C. (Assume AH to be temperature independent) (e) Calculate the degree of dissociation, a, of...