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Total: 8 Question 5 Using the fundamental commutator relation show that la a+] = 1 Show...
5) a) Beginning with the fundamental relation, dE = TDS – PdV, show that S = S(E,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
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)
Question 8
Let R be relation on a set A. 1. When is R said to be an equivalence relation? Give a precise definition, using appropriate quantifiers etc. 2. When is R said to be an partial order? Give a precise definition, using appropriate quantifiers etc (You don't need to redefine things that you defined in the previous part... you may simply mention them to save time.) 3. On Z, define a relation: a D biff a - b is...
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.
solve using the fundamental law of calculus if
applicable
Evaluate the definite integral La 2e (Inx) dx x
2. (9 points total) Uncertainty relations. a) (1 point) Compute the commutator of the operators of coordinate and momentum in one dimension. b) (1 point) Two Hermitian operators A and B satisfy the relation [A, B] = iſ, where I is a number. Prove that I' is real. c) (1 point) Give the definition of the uncertainties A A and A B. d) (2 points) In this and subsequent parts of the question, we consider a normalized quantum stately) with...
Question 17 (9 points) (a) Label the parts of the DC motor. (5 marks) 1 2 3 5 (b) Explain the Motor Principle in relation to the operation of the DC motor. ( marks) (c) Explain the role of the commutator in the DC motor. (2 marks)
8. (a) (10%) Start from the fundamental equation of du and Tey = ), show that ttp = T ). - p. (b) (10%) Using the equation in (a), show that Typ = for van der Waal gas. Use the blank sheet to show the processes. Vm
Consider the following system of equations. orie 10 x = 5 la (a) Find a fundamental matrix for the given system of equations. (t) = Equation Editor Common 12 Matrix sin(a) cos(a) tan(a) seca) osca) cot(a) de lidz jjar vayalal U s in(a) cos(@) tana ) (b) Find the fundamental matrix (t) satisfying • (0) = I. (t) = Equation Editor Common 2 Matrix cos(a) tan(a) sin(a) seca) sin- (@) sec(a) csele) cot(a) den ſide | saz cos @) tan-(a)