Homework Answers
where U=Internal energy,
S=Entropy, H=Enthalpy, P=Pressure, V=Volume, T=Temperature.
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Maxwell's Relations < 6 of 15 > In thermodynamics, the variables T V, P, and n...
(Thermodynamics, Maxwell relations. Mathematics) 3 Consider the microcanonical formula for the equilibrium energy E(S, V,N) of...
(Thermodynamics, Maxwell relations. Mathematics) 3 Consider the microcanonical formula for the equilibrium energy E(S, V,N) of some general system.58 One knows that the second deriva- tives of E are symmetric; at fixed N, we get the same answer whichever order we take partial derivatives with respect to S and V (a) Use this to show the Marwell relation (3.70) OS S,N (This should take two lines of calculus or less.) Generate two other similar formulae by taking other second partial...
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 .
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 .
Derive F, P,U, and Cv in terms of N, V, T and constants for the Ideal...
Derive F, P,U, and Cv in terms of N, V, T and constants for the Ideal Gas partition function Q(N,V,T) = V^N / (L^(3N)*N!), where L = h/sqrt(2*pi*m*kB*T)
Question 10 Statistical thermodynamics may be used to find the radiation pressure P for cavity (or...
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:...
1 The Gibbs Paradox Consider N particles, each of mass m, in a 3-dimensional volume V at temperature T. Each particle i...
1 The Gibbs Paradox Consider N particles, each of mass m, in a 3-dimensional volume V at temperature T. Each particle i has momentum pi. Assume that the particles are non-interacting (ideal gas) and distinguishable. a) (2P) Calculate the canonical partition function N P for the N-particle system. Make sure to work out the integral. b) (2P) Calculate the free energy F--kBTlnZ from the partition function Z. Is F an extensive quantity? c) (2P) Calculate the entropy S F/oT from...
Problem 10.33 Complete the following table for an ideal gas: P V n T 2.10 atm...
Problem 10.33 Complete the following table for an ideal gas: P V n T 2.10 atm 1.20 L 0.520 mol ? K 0.320 atm 0.270 L ? mol 32 ∘C 660 torr ? L 0.335 mol 370 K ? atm 595 mL 0.270 mol 280 K Part A Complete the first row of the table. T = 59.1 K SubmitMy AnswersGive Up Correct Significant Figures Feedback: Your answer 59.02 K was either rounded differently or used a different number of...
3,9? Part I: Choose five of these questions. (12 points each) Ana 1. Here is the...
3,9?
Part I: Choose five of these questions. (12 points each) Ana 1. Here is the van der Waals Equation for one mole of gas: P -by vary with dV and dT? Bethe Given this equation, how does the infinitesimal change in pressure, dl. as specific as possible. (In other words, evaluate the derivatives.) andard 2. A sample of gas molecules of density D N / Vwhere N is the numbe volume) is moving with a speed y, in the...
Find the Laplace Transformation (10 points) u(t) (10 points) eu(t) (10 points) 30 cos wt u(t)...
Find the Laplace Transformation (10 points) u(t) (10 points) eu(t) (10 points) 30 cos wt u(t) Use this ental infor- vorewo Pekes 1e of 500 K. Obtain a numerical value, includ- ing units, for each of the following partial derivatives for this gas. he values which the concentration of the andioen- antibody complex will be equal to the concen- tration of the unbound antibody. perimen- plies that consider- aG (b) (a) aT 19. The isomerization of glucose-6-phosphate G6P) to fructose-6-phosphate...
(Thermodynamics, Maxwell relations. Mathematics) 3 Consider the microcanonical formula for the equilibrium energy E(S, V,N) of some general system.58 One knows that the second deriva- tives of E are symmetric; at fixed N, we get the same answer whichever order we take partial derivatives with respect to S and V (a) Use this to show the Marwell relation (3.70) OS S,N (This should take two lines of calculus or less.) Generate two other similar formulae by taking other second partial...
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:...
1 The Gibbs Paradox Consider N particles, each of mass m, in a 3-dimensional volume V at temperature T. Each particle i has momentum pi. Assume that the particles are non-interacting (ideal gas) and distinguishable. a) (2P) Calculate the canonical partition function N P for the N-particle system. Make sure to work out the integral. b) (2P) Calculate the free energy F--kBTlnZ from the partition function Z. Is F an extensive quantity? c) (2P) Calculate the entropy S F/oT from...
3,9?
Part I: Choose five of these questions. (12 points each) Ana 1. Here is the van der Waals Equation for one mole of gas: P -by vary with dV and dT? Bethe Given this equation, how does the infinitesimal change in pressure, dl. as specific as possible. (In other words, evaluate the derivatives.) andard 2. A sample of gas molecules of density D N / Vwhere N is the numbe volume) is moving with a speed y, in the...
Find the Laplace Transformation (10 points) u(t) (10 points) eu(t) (10 points) 30 cos wt u(t) Use this ental infor- vorewo Pekes 1e of 500 K. Obtain a numerical value, includ- ing units, for each of the following partial derivatives for this gas. he values which the concentration of the andioen- antibody complex will be equal to the concen- tration of the unbound antibody. perimen- plies that consider- aG (b) (a) aT 19. The isomerization of glucose-6-phosphate G6P) to fructose-6-phosphate...
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