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Consider a homogeneous mixture of two ideal monatomic gases, at temperature T ,
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Obtain an expression for the entropy per particle, in terms of temperature and density,
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Consider a quantum ideal gas inside a cubic vessel of side 5, and suppose that the orbitals of the particles are associated with wave functions that vanish at the surfaces of the cube
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Show that the entropy of an ideal quantum gas may be written as
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Show that the average quadratic deviation of energy in the grand canonical ensemble may be written as
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Obtain the grand partition function of a classical system of particles, inside a container of volume V , given by the Hamil- tonian
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Show that the entropy in the grand canonical ensemble can be written as
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Find a basis for the vector space P3 composed of eigenvectors of the linear transfor- mation T . Then find a matrix representation of T relative to this basis
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In Example CBCV we computed the vector representation of y relative to C,
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Create an entirely different proof of Theorem IMILT that relies on Definition IVLT to establish the invertibility of T , and that relies on Definition MI to establish the invertibility of A
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Suppose U and V are vector spaces. Define the function Z :
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Theorem DCP tells us that the characteristic polynomial of a square matrix of size n has degree n
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Suppose that U is a unitary matrix with eigenvalue λ. Prove that λ has modulus 1,
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