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شرح قوانين thermodynamic
0. If two systems are in thermal equilibrium with a third system, then they must be in thermal equilibrium with each other. 1. http://scienceworld.wolfram.com/physics/timg81.gif, where dE is the energy change, http://scienceworld.wolfram.com/physics/timg83.gif 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 http://scienceworld.wolfram.com/physics/timg87.gif. 3. As temperature goes to 0, the entropy S approaches a constant http://scienceworld.wolfram.com/physics/timg88.gif. 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 http://scienceworld.wolfram.com/physics/fimg129.gif, 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. |
Conservation of Energy
If the forces acting on a particle are conservative so that there exists a function http://scienceworld.wolfram.com/physics/cimg270.gif such that then the total energy given as the sum of kinetic energy and potential energy is a constant |
Energyhttp://scienceworld.wolfram.com/imag...b_topright.gif
http://scienceworld.wolfram.com/imag...dient-teal.gifhttp://scienceworld.wolfram.com/images/spacer.gifhttp://scienceworld.wolfram.com/images/spacer.gif 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 |
Conservation of Energyhttp://scienceworld.wolfram.com/imag...b_topright.gif
http://scienceworld.wolfram.com/imag...dient-teal.gifhttp://scienceworld.wolfram.com/images/spacer.gifhttp://scienceworld.wolfram.com/images/spacer.gif If the forces acting on a particle are conservative so that there exists a function http://scienceworld.wolfram.com/physics/cimg270.gif such that then the total energy given as the sum of kinetic energy and potential energy is a constant. |
Energy Densityhttp://scienceworld.wolfram.com/imag...b_topright.gif
http://scienceworld.wolfram.com/imag...dient-teal.gifhttp://scienceworld.wolfram.com/images/spacer.gifhttp://scienceworld.wolfram.com/images/spacer.gif 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. |
Heat
The first law of thermodynamics where http://scienceworld.wolfram.com/physics/himg113.gif is the heat change, dE is the energy change, http://scienceworld.wolfram.com/physics/himg115.gif 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 http://scienceworld.wolfram.com/physics/himg118.gifhttp://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg119.gif(2) http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg120.gif http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg121.gif(3) http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg122.gif http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg123.gif http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg124.gif(4) where http://scienceworld.wolfram.com/physics/himg125.gif is the heat capacity at constant pressure, http://scienceworld.wolfram.com/physics/himg126.gif is the thermal expansion coefficient, and http://scienceworld.wolfram.com/physics/himg127.gif is the isothermal bulk modulus. At constant pressure, http://scienceworld.wolfram.com/physics/himg128.gifhttp://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg129.gif(5) http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg130.gif http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg131.gif(6) http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg132.gif (7) http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg133.gif http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg134.gif(8) where http://scienceworld.wolfram.com/physics/himg135.gif 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 http://scienceworld.wolfram.com/imag.../biography.gif 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 http://scienceworld.wolfram.com/imag.../biography.gif 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. |
Combined Law of Thermodynamics
For energy E, temperature T, pressure P, and volume V, Entropyhttp://scienceworld.wolfram.com/imag...b_topright.gif Entropy is a measure of the disorder of a system, and is defined by where http://scienceworld.wolfram.com/physics/eimg114.gif is the number of states of a system. In terms of the partition function Z, |
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. Equilibriumhttp://scienceworld.wolfram.com/imag..._downarrow.gif Equilibrium Constanthttp://scienceworld.wolfram.com/imag...b_topright.gif The equilibrium constant for a chemical reaction is given by where http://scienceworld.wolfram.com/physics/eimg352.gif is the Helmholtz free energy, k is the Stefan-Boltzmann constant, and T is the temperature Helmholtz Free Energyhttp://scienceworld.wolfram.com/imag...b_topright.gif The Helmholtz free energy is defined by 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 If T and V are constant, the (2) reduces to But the combined law of thermodynamics states that and, since we have stipulated dV = 0, this becomes Therefore The Helmholtz free energy is intimately related to the equilibrium constant at constant volume http://scienceworld.wolfram.com/physics/himg193.gif via 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 http://scienceworld.wolfram.com/physics/himg195.gifenergy, commonly denoted |
Equilibrium Postulatehttp://scienceworld.wolfram.com/imag...b_topright.gif
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 http://scienceworld.wolfram.com/physics/mimg207.gif is the applied force and http://scienceworld.wolfram.com/physics/mimg208.gif 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 |
Thermodynamic Lawshttp://scienceworld.wolfram.com/imag...b_topright.gif
0. If two systems are in thermal equilibrium with a third system, then they must be in thermal equilibrium with each other. 1. http://scienceworld.wolfram.com/physics/timg81.gif, where dE is the energy change, http://scienceworld.wolfram.com/physics/timg83.gif 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 http://scienceworld.wolfram.com/physics/timg87.gif. 3. As temperature goes to 0, the entropy S approaches a constant http://scienceworld.wolfram.com/physics/timg88.gif. Combining the first and second laws gives the combined law of thermodynamics |
Third Law of Thermodynamics
As temperature goes to 0, the entropy S approaches a constant http://scienceworld.wolfram.com/physics/timg88.gif. Furthermore, it guarantees that the entropy of a pure, perfectly crystalline substance is 0 if the absolute temperature is 0. |
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