Paramagnetic materials present a magnetic behavior described by Curie's equation:
where M is the magnetization of the material, H is the external magnetic field in Tesla, C is a constant and T is the temperature.
(a) Indicate whether M and H are intensive or extensive properties. Explain.
(b) Write the form of the configuration work, dw, for this system.
(c) Find an expression for the work that has to be done on the system to change its magnetization from 0 to M.
Homework Answers
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Paramagnetic materials present a magnetic behavior described by
Curie's equation:
where M is the magnetization of...
Consider a canonical ensemble of ? paramagnetic particles of magnetic moment ? in an external magnetic...
Consider a canonical ensemble of ? paramagnetic particles of
magnetic moment ? in an external magnetic field B and find
a. An expression for the average magnetic moment per
particle
b. The total magnetization.
c. Demonstrate the Curie’s law of paramagnetism that predicts
that at high temperature the magnetization of the material is
proportional to the ratio between the external field and the
temperature
Consider a canonical ensemble of N paramagnetic particles of magnetic moment μ in an external magnetic...
06) Suppose a paramagnetic system that is under the action of an auxiliary (magnetic) field H....
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....
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...
Problem4: For á magnetic substance, thethermodynamie variables are the intensive magnetic fielH, and theextensive magnetization M,which...
Problem4: For á magnetic substance, thethermodynamie variables are the intensive magnetic fielH, and theextensive magnetization M,which are unidirectional and uniform in space. Since the work done by the magnetic system is given by dW-HdM we can compare it withdW PdV to determine the correspondence between the pairs of variables (H.M and (P.V). Write down the corresponding first law for a magnetic system where the number of particles is constant. Use your understanding of the ideal gas systems for the rest...
has a magnetic field 거 which induces magnetization of the material M. I he tree is...
has a magnetic field 거 which induces magnetization of the material M. I he tree is Assume constant temperature so (a) Derive a Maxwell relationship between the magnetic field and the volume. aoes hot ma (b) Make a Legendra transformation from G(P, M) to G'(P, H) and express dG. dar (c) Use G' to derive an expression for d P dH at equilibrium (dG-0). What does this mean physically?
2) In class we discussed how non-interacting spins align with an external magnetic field. For quantum...
2) In class we discussed how non-interacting spins align with an external magnetic field. For quantum spins in three dimensions the magnetization can be written HeffB М 3 пиеg B, (а), а — Heff = g)where kвт 2J+1 coth (acotha 2J+1 :a) is the Brillouin function В (а) 2J 2J JU+1)+S(S+1)+L (L+ 1) and g 1 is the Lande g-factor 2J+1) Here will specialize to the case J1/2 (L=0, S=1/2). a) Calculate the Lande g-factor for this case b) Starting...
summatize the following info and break them into differeng key points. write them in yojr own...
summatize the following info and break them into differeng key points. write them in yojr own words
apartus
6.1 Introduction—The design of a successful hot box appa- ratus is influenced by many factors. Before beginning the design of an apparatus meeting this standard, the designer shall review the discussion on the limitations and accuracy, Section 13, discussions of the energy flows in a hot box, Annex A2, the metering box wall loss flow, Annex A3, and flanking loss, Annex...
summarizr the followung info and write them in your own words and break them into different...
summarizr the followung info and write them in your own words and break them into different key points. 6.5 Metering Chamber: 6.5.1 The minimum size of the metering box is governed by the metering area required to obtain a representative test area for the specimen (see 7.2) and for maintenance of reasonable test accuracy. For example, for specimens incorporating air spaces or stud spaces, the metering area shall span an integral number of spaces (see 5.5). The depth of...
What are the instruments that have been utilized for the review article discussions? ` 1. Introduction...
What are the instruments that have been utilized for the
review article discussions?
`
1. Introduction In recent years, nanoclays have been the object of particular interest for many scientists and researchers in chemistry, physics, engineering and biology due to their excellent properties as well as their sustain- ability [1-3]. For instance, they represent the starting point to the de velopment of smart materials for drug delivery (4-9), food packaging [10-12), environmental remediation and wastewater treatment [13], cultural heritage [14–17and...
10. Write a one-page summary of the attached paper? INTRODUCTION Many problems can develop in activated...
10. Write a one-page summary of the attached paper? INTRODUCTION Many problems can develop in activated sludge operation that adversely affect effluent quality with origins in the engineering, hydraulic and microbiological components of the process. The real "heart" of the activated sludge system is the development and maintenance of a mixed microbial culture (activated sludge) that treats wastewater and which can be managed. One definition of a wastewater treatment plant operator is a "bug farmer", one who controls the aeration...
Consider a canonical ensemble of ? paramagnetic particles of
magnetic moment ? in an external magnetic field B and find
a. An expression for the average magnetic moment per
particle
b. The total magnetization.
c. Demonstrate the Curie’s law of paramagnetism that predicts
that at high temperature the magnetization of the material is
proportional to the ratio between the external field and the
temperature
Consider a canonical ensemble of N paramagnetic particles of magnetic moment μ in an external magnetic...
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...
Problem4: For á magnetic substance, thethermodynamie variables are the intensive magnetic fielH, and theextensive magnetization M,which are unidirectional and uniform in space. Since the work done by the magnetic system is given by dW-HdM we can compare it withdW PdV to determine the correspondence between the pairs of variables (H.M and (P.V). Write down the corresponding first law for a magnetic system where the number of particles is constant. Use your understanding of the ideal gas systems for the rest...
has a magnetic field 거 which induces magnetization of the material M. I he tree is Assume constant temperature so (a) Derive a Maxwell relationship between the magnetic field and the volume. aoes hot ma (b) Make a Legendra transformation from G(P, M) to G'(P, H) and express dG. dar (c) Use G' to derive an expression for d P dH at equilibrium (dG-0). What does this mean physically?
2) In class we discussed how non-interacting spins align with an external magnetic field. For quantum spins in three dimensions the magnetization can be written HeffB М 3 пиеg B, (а), а — Heff = g)where kвт 2J+1 coth (acotha 2J+1 :a) is the Brillouin function В (а) 2J 2J JU+1)+S(S+1)+L (L+ 1) and g 1 is the Lande g-factor 2J+1) Here will specialize to the case J1/2 (L=0, S=1/2). a) Calculate the Lande g-factor for this case b) Starting...
summatize the following info and break them into differeng key points. write them in yojr own words
apartus
6.1 Introduction—The design of a successful hot box appa- ratus is influenced by many factors. Before beginning the design of an apparatus meeting this standard, the designer shall review the discussion on the limitations and accuracy, Section 13, discussions of the energy flows in a hot box, Annex A2, the metering box wall loss flow, Annex A3, and flanking loss, Annex...
What are the instruments that have been utilized for the
review article discussions?
`
1. Introduction In recent years, nanoclays have been the object of particular interest for many scientists and researchers in chemistry, physics, engineering and biology due to their excellent properties as well as their sustain- ability [1-3]. For instance, they represent the starting point to the de velopment of smart materials for drug delivery (4-9), food packaging [10-12), environmental remediation and wastewater treatment [13], cultural heritage [14–17and...
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