شرح قوانين thermodynamic

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0. If two systems are in thermal equilibrium with a third system, then they must be in thermal equilibrium with each other. 1. , where dE is the energy change, is the change in heat, dW is the work done, T is the temperature, dS is the change in entropy, P is the pressure, and dV is the volume change. 2. The second law of thermodynamics prohibits the construction of a perpetual motion machine of `the second kind.' A consequence is the result that . 3. As temperature goes to 0, the entropy S approaches a constant . Combining the first and second laws gives the combined law of thermodynamics

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The first law of thermodynamics is a consequence of conservation of energy and requires that a system may exchange energy with the surroundings strictly by heat flow or work. Therefore, for change in energy dE, heat change , work done dW,

For a reversible process in which only expansive work is considered, the first law takes the form

where T is the temperature, dS the entropy change, P the pressure, and dV volume change.

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Conservation of Energy


If the forces acting on a particle are conservative so that there exists a function such that

then the total energy

given as the sum of kinetic energy and potential energy is a constant

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Energy

Energy is an abstract quantity of extreme usefulness in physics because it is defined in such a way that the total energy of any closed physical system is always constant (conservation of energy). It is impossible to overstate the importance of this concept in all branches of physics from elementary mechanics to general relativity. Energy is measured in units of mass times velocity squared, and the MKS and cgs units of energy are the Joule and erg, respectively. Other common units of energy include the Btu, calorie, and kilowatt hour.

The important quantity in physics known as work, which is the product of applied force over a distance, has units of energy. In fact, the notion that heat is a form of energy was one of the most important developments in classical physics and thermodynamics. Energy is related to power P emitted over a time t by

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Conservation of Energy

If the forces acting on a particle are conservative so that there exists a function such that

then the total energy

given as the sum of kinetic energy and potential energy is a constant.

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Energy Density
Energy density is the amount of energy stored in a given system or region of space per unit volume, and is most commonly denoted u. It therefore has units of energy per length cubed.

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Energy Flux

(1)

The mean energy flux is , also written as and called I, the intensity. For a traveling wave,

(2)

The unit of energy flux is 1 J m-2 s-1 = 1 kg s-3. For radiation, consider a half-plane filled with energy density u, then

(3)

where c is the speed of light, is the angle from the propagation axis, a is the radiation constant, T is the temperature, and is the Stefan-Boltzmann constant












Foot Pound


A unit of energy equal to

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Heat



The first law of thermodynamics

(1)

where is the heat change, dE is the energy change, is the work done, P is the pressure, dV is the volume change, T is the temperature, and dS is the entropy change, can be written at constant volume as

(2) (3) (4)

where is the heat capacity at constant pressure, is the thermal expansion coefficient, and is the isothermal bulk modulus.

At constant pressure,

(5) (6) (7) (8)

where is the heat capacity at constant volume.

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Second Law of Thermodynamics

The second law of thermodynamics prohibits the construction of a perpetual motion machine "of the second kind." There are two usual statements of this law. Kelvin's formulation states that it is impossible for a system operating in a cycle and in contact with one thermal reservoir to perform positive work in the surroundings. Clausius's formulation states that it is impossible for a system operating in a cycle to produce positive heat flow from a colder body to a hotter body.

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Combined Law of Thermodynamics


For energy E, temperature T, pressure P, and volume V,

Entropy





Entropy is a measure of the disorder of a system, and is defined by

(1)

where is the number of states of a system. In terms of the partition function Z,

(2)

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Reversible Process


A reversible process is one in which the timescale is assumed to be so slow that every intermediate state deviates only infinitesimally from equilibrium. Every intermediate state is exactly described by a set of macroscopic thermodynamic variables and may be assumed to be at equilibrium. Since every intermediate state is exactly known, the process may be reversed at an infinitesimally slow rate. This may be simply illustrated by imagining a cylinder with a frictionless piston on the top. Further imagine that there is a quantity of sand on top of the piston. A good approximation to a reversible process would be realized by removing the sand one grain at a time and carefully recording the thermodynamic variables (temperature and pressure in this case) after each grain of sand is removed. This would be a reversible expansion and one could individually return the grains of sand one at a time and reproduce each intermediate state exactly, thus reversing the transformation.
Equilibrium

Equilibrium Constant




The equilibrium constant for a chemical reaction is given by

where is the Helmholtz free energy, k is the Stefan-Boltzmann constant, and T is the temperature

Helmholtz Free Energy




The Helmholtz free energy is defined by

(1)

where E is the energy, T is the temperature, and S is the entropy. When a system changes its thermodynamic state, the change in Helmholtz free energy is therefore given by

(2)

If T and V are constant, the (2) reduces to

(3)

But the combined law of thermodynamics states that

(4)

and, since we have stipulated dV = 0, this becomes

(5)

Therefore

(6)

The Helmholtz free energy is intimately related to the equilibrium constant at constant volume via

(7)

where k is Boltzmann's constant. A system with fixed external parameters in thermal contact with a heat reservoir at equilibrium has a minimum Helmholtz free energy, commonly denoted

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Equilibrium Postulate


An isolated system in equilibrium is equally likely to be in any of its accessible states


Mechanical Equilibrium

A system is said to be in mechanical equilibrium if

where is the applied force and is the virtual displacement


Floating


Homogeneous spheres float stably in all possible orientations (Ulam 1960), but it has never been proved that no other homogeneous body shares this property (Gilbert 1991).

When the two above shapes have uniform density 0.5 they, like the uniform sphere of density 1, will float in a liquid in any orientation without tending to rotate (Mauldin 1982, Wells 1991, Gilbert 1991

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Thermodynamic Laws



0. If two systems are in thermal equilibrium with a third system, then they must be in thermal equilibrium with each other. 1. , where dE is the energy change, is the change in heat, dW is the work done, T is the temperature, dS is the change in entropy, P is the pressure, and dV is the volume change. 2. The second law of thermodynamics prohibits the construction of a perpetual motion machine of `the second kind.' A consequence is the result that . 3. As temperature goes to 0, the entropy S approaches a constant . Combining the first and second laws gives the combined law of thermodynamics

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Third Law of Thermodynamics

As temperature goes to 0, the entropy S approaches a constant . Furthermore, it guarantees that the entropy of a pure, perfectly crystalline substance is 0 if the absolute temperature is 0.