Consider a system with magnetic dipole moment u in a static magnetic field B. This system is in thermal equilibrium at absolute temperature T. Consider that the magnetic field applied to the system changes by a dB in an infinitesimal semi-stationary process. In this case, remember that the mechanical work done is as much as - udB. The following definitions for this system use. (E = internal energy, S = entropy): Enthalpy: H = E-µB. Helmholtz free energy: F = E - TS. A) In this system, write dE in differential form, assuming entropy S and magnetic field B as independent parameters and combining the first and second law of thermodynamics. B) Using the results of (a) and the differential forms, express the temperature T and the magnetic dipole moment u in terms of the partial derivatives of E. C) Using the properties of partial derivatives and the results of (b), express the Maxwell connections for this system by taking the appropriate partial derivatives of T and u.

Consider a system with magnetic dipole moment u in a static magnetic field B. This system is in thermal equilibrium at absolute temperature T. Consider that the magnetic field applied to the system changes by a dB in an infinitesimal semi-stationary process. In this case, remember that the mechanical work done is as much as - udB. The following definitions for this system use. (E = internal energy, S = entropy): Enthalpy: H = E-µB. Helmholtz free energy: F = E - TS. A) In this system, write dE in differential form, assuming entropy S and magnetic field B as independent parameters and combining the first and second law of thermodynamics. B) Using the results of (a) and the differential forms, express the temperature T and the magnetic dipole moment u in terms of the partial derivatives of E. C) Using the properties of partial derivatives and the results of (b), express the Maxwell connections for this system by taking the appropriate partial derivatives of T and u.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A 75 W light bulb is used for 12 hours a day. The electricity for this bulb comes from a natural gas fired power plant that operates with 49% efficiency. How much CO₂ is emitted per day to power this light bulb? Make a simple estimate of the CO2 emissions from the power plant, ignoring transmission losses. 0.0024 kg CO2/day Xx 0.0024 We mentioned earlier in the course that energy technologies in developing countries often have much lower efficacies than those in developed countries. Let's look at one example, lighting via kerosene lamps, which are common in developing countries but about 150x less effective than incandescent lightbulbs at turning energy into useful light. If a family wanted just one tenth of the light provided by the 75 W lightbulb, they'd need to consume 15x as much power, or 1125 W. If a family ran 1125 W worth of kerosene lamps for just 2 hours each day, how much CO2 would this emit? You may assume that kerosene produces the same emissions as gasoline. 3.00 kg…
Answer the ff and show complete solution:
A system of 7,542 particles initially has 5.44 x 1039 possible configurations. If we remove some of the particles and are left with 2,118 particles in the system what is the change in entropy? You can assume the number of possible configurations does not change.Please express answer in scientific notation to the second decimal place
The specific heat capacity of water is the amount of energy (in Joules) required to raise the temperature of 1 kg of water by 1 °C; for practical purposes, this is equal to J kg. C about 4186 You put 0.5 L of water in a microwave oven. The water has a starting temperature of 4 °C. The microwave oven is rated at at 1,400 W and efficiency of 53%. If you run the microwave for 35 seconds, what is the temperature of the water when the microwave oven stops? Assume that the density of water is p=1 kg/L. Your Answer:
A small metal cube with a thermal mass mc and an initial temperature 0 is dropped into a container of water that is actively maintained at a constant temperature 0w. The cube quickly comes to rest on the bottom surface of the container. The bottom surface is maintained at a constant temperature 0 (note that this is different from 0w). The thermal resistance between the cube and the water is Rcw while the thermal resistance between the bottom surface of the container and the cube is RCB. The temperature of the cube is denoted by 0c. a) Draw the system schematic indicating the assumed directions of the heat transfer rates. Label all the nodes and system parameters. b) Derive the governing equation for the temperature of the cube, 0c. c) Where does to appear in the system schematic and how does it affect the governing equations? d) Calculate the steady-state temperature of the cube, css, assuming the following system parameters: 0o = 21°C, 0B = 6°C, 0w = 0°C, Rcw = 2°C/W, and RCB = 4°C/W
a) Find the difference of molar-specific heats Cp - C, for the gas covered by the equation of state: (P+) (V - b) = RT b) Determine the volume of the hypersphere in N-dimensional space. c) An ideal gas consists of N monatomic molecules. Using the grand canonical ensemble, (T-μ) distribution, calculate the chemical potential, pressure, and entropy.
Which of the following statements about the Gibbs function (Gibbs free energy) are generally true? Select one or more: a. The minimization of the Gibbs function in thermodynamic equilibrium (under the right conditions) is a consequence of the maximization of the entropy of the considered system. b. The minimization of the Gibbs function in thermodynamic equilibrium is a consequence of the maximization of the total entropy of the system and the environment. C. The Gibbs function is minimized in thermodynamic equilibrium for a system whose temperature T, volume V and number of particles N are constant. d. The Gibbs function is minimized in thermodynamic equilibrium for a closed system whose temperature T and pressure p are constant.
b. From the temperature dependence of surface tension, researchers concluded that the entropy of the surface layer of water is 157x10 J/K per m. How much (negative) tension does this excessive entropy create? Assume T 300K and express this entropic component of tension in mN/m.
Problem #2: For this problem, one mole of a diatomic ideal gas is taken around a reversible cycle by starting at pressure P, volume V, and temperature T, then in an isochoric process 1 increasing pressure to 6P, then in an isobaric process 2 increasing its volume to 21V, then another isochoric process 3 back to a pressure P, and finally in an isobaric process 4 back to P, V, T. Find the temperature of this gas at the end of process 1, 2, and 3 in terms of the original temperature T. Find the internal energy change in process 1 and in process 2 in terms of P and V. Find the heat transfer in process 1 and in process 2 in terms of P and V.
The first law of thermodynamics is generally thought to be the least demanding to grasp, as it is an extension of the law of conservation of energy, meaning that energy can be neither created nor destroyed. (a) The variations of properties during phase change processes are best studied and understood with the help of property diagrams. Point out schematically the difference between the P-v diagram in respective of: 1. contracts on freezing. ii. expands on freezing.
a. Find an appropriate expression for the change in entropy in the following two cases: 1) S=S(T, V) 2) s= S(T, P) Where: S is entropy, T is temperature, V is volume, P is pressure b. Prove the following two themodynamie property relationships (똥),-() 8C, Where: T, P. V are temperature, pressure and volume, respectively. C, and C, are specific heats at constant volume and constant pressure, respectively.
Please I want answer of this question. Many Thanks Note: Z is (27)