5) a) Beginning with the fundamental relation, dE = TDS – PdV, show that S =...
5) a) Beginning with the fundamental relation, dE = Tds - PdV, show that S = S(E, D) b) Use the answer to part a to show that: c) Legendre transform S with respect to the conjugate variables (E to obtain the Helmholtz free entropy s and show that the resulting expression for dø indicates that ° = .D Note: The expression dE = Tds - PdV is sufficient proof that E = E(S.V)
Need complete answer for part B 5) a) Beginning with the fundamental relation, dE = TdS - PdV, show that S = S(E,V) b) Use the answer to part a to show that: as 1 аnd as P ӘЕ. V
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 .
A=U-TS is Helmholtz free energy, which is commonly used in statistical thermodynamics. Starting from dU=TdS-pdV, show that dA=-SdT-pdV
Total: 8 Question 5 Using the fundamental commutator relation show that la a+] = 1
A mixture of two monatomic ideal gases consists of Na molecules of gas A and Na molecules of gas B in a container of volume V at temperature T. (a) Obtain an expression for natural log of the number of the accessible microstates for each species (ie, ln S, and In Ω), (b) Show that the entropy of the mixture system is 4. EA and Ea are the total energies for the two molecular species, m, and m , the...
We are trying to show entropy gives rise to presssure. Imagine a box with volume V is divided into M smaller cubic boxes with volume Vo and N particles are distributed in the box. Assuming N << M, show that P=TdS/dV can be approximated to P=NkBT/V, where V=VoxM more so, S=KblnW(N:M) and that the first law of thermo is TdS=U+PdV-udN, but N and U are constants
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,...
5. (25 points For credit; show every step in the derivations. (a) Starting with the Fundamental Equation for U determine the associated partial derivatives for T and P. Next, determine the associated Maxwell Relation. (b) Starting with the Helmholtz free energy (A = U – TS) derive the associated Fundamental Equation and identify the partial derivative relationships for P and S. Then derive the associated Maxwell Relation.
5. s a de current and In the circuit shown in Fig. P e, is a sinusoidal signal. Capacitors C, and C, are very large; their function is to couple the signal to and from the diode but block the de current from flowing into the signal source or the load (not shown). Use the diode small-signal model to show that the signal component of the output voltage is V, If v, = 10mV, find v, for 1 = 1...