Consider the thermodynamic identity
dU= TdS – PdV + μdN .
Identify each term in the thermodynamic identity. Derive the thermodynamic identity for G,
dG = -SdT – PdV + μdN .
Consider the thermodynamic identity dU= TdS – PdV + μdN . Identify each term in...
A=U-TS is Helmholtz free energy, which is commonly used in statistical thermodynamics. Starting from dU=TdS-pdV, show that dA=-SdT-pdV
Many times it is useful re-writing partial differential thermodynamic expressions in different forms using the total differentials for E, H, F. and G. The total differentials of E, H, F, and G are: dE = TDS – PdV + udn dH = TDS + VDP + udn dF = -SDT – PdV + udn dG = -SDT + VdP + udn - Part A Rewrite the following expression in terms of S, T, P, V.1, 11, Q, CAm, and/or Cvm,...
By considering the volume V and entropy S as the two independent variables in the thermodynamic equation dE = TdS−PdV , derive the Maxwell relation between the derivatives ∂T/ ∂V and ∂P/ ∂S .
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
9. Derive the equation dH = TDS + VdP and show tha ASm = Cp.m In 2 - R In For the change of one mole of an ideal gas from Tu, P, to T2, P, assuming that Cp,m is independent of temperature. (Hint: Start from dU = Tds - pdV and consider what you need to add to both sides to get an expression for dH on the left side).
Answer the following questions
A. Multiple Choices (16 point each) 1. Which of the following is stro (A) , AS (B) 4. 0, AS (C) , AS (D) 4. 0, AS 2. Consider the following reaction NH.NO, OS) HOD) NIN Which of the following is (ar) true about this reaction GUNAH (A) the reaction is endothermis c hungsbe (B) This reaction must use the entry of the universet (C) This reaction is spontaneously low temperature (D) This reaction will reaction...
(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...
02) Consider a hydrostatic system represented by the thermodynamic variables volume V, pressure P and temperature T. a) Consider entropy S = S(T, V) and derive the equation TdS. Tas = Cvat +T (1) dV. V Show that this equation can be written as follows BT TdS = CydT + PDV where Cv is the thermal capacity at constant volume, B is the isobaric expansiveness and K is isothermal compressibility: b) Consider a gas described by the equation of state...
06) Suppose a paramagnetic system that is under the action of an auxiliary (magnetic) field H. Thus, the work involved, it has to be that the work involved in a reversible process is described as đW = 10Hdm. where m is the total magnetic dipole moment of the system and u0 is the magnetic permeability of the vacuum. a) Determine the expression of the differential du of the internal energy U and indicate the two independent natural variables associated with...
06) Suppose a paramagnetic system that is under the action of an auxiliary (magnetic) field H. Thus, the work involved, it has to be that the work involved in a reversible process is described as đW = 10Hdm. where m is the total magnetic dipole moment of the system and u0 is the magnetic permeability of the vacuum. a) Determine the expression of the differential du of the internal energy U and indicate the two independent natural variables associated with...