define and explain the law of equipartion of energy
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The law of equipartition of energy is a law in thermodynamics which says this:
Suppose you supply some quantity of energy to a system. Then the supplied energy is distributed equal among all the degrees of freedom. The degrees of freedom are the minimum number of coordinates required to specify the state of a system completely. For example if I have a monotomic gas molecule in three dimensional space, then it would have the degrees of freedom, along x,y,z address. For a polyatomic gas molecule, the number of degrees of freedom N can be calculated by: N=3A−RN=3A−R where AA is the number of atoms in a molecule and RR is the number of constraints in the molecule (you can take it as the number of bonds).
Coming back to your question, the kinetic energy of a molecule of a gas according to kinetic theory of gases is given by: mv²/2=3KT/2mv²/2=3KT/2 where M is the mass of the molecule, v is the RMS velocity of the molecule and k is the Boltzmann constant =1.38×10−²³J/K.=1.38×10−²³J/K. Rewriting the above equation, mv(x)²/2+mv(y)²/2+mv(z)²/2=KT/2+KT/2+KT/2mv(x)²/2+mv(y)²/2+mv(z)²/2=KT/2+KT/2+KT/2
Here v(x)v(x) means the x component of the RMS velocity, v(y)v(y) means y component of RMS velocity, and the same goes with v(z).v(z). Now clearly from this equation, energy supplied to the system by means of temperature enters into the system and each degree of freedom (co-ordinate) of the molecule gets an equal KT/2KT/2 amount of energy. This is the meaning of law of equipartition of energy.....
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The law of equipartition of energy is a law in thermodynamics which says this:
Suppose you supply some quantity of energy to a system. Then the supplied energy is distributed equal among all the degrees of freedom. The degrees of freedom are the minimum number of coordinates required to specify the state of a system completely. For example if I have a monotomic gas molecule in three dimensional space, then it would have the degrees of freedom, along x,y,z address. For a polyatomic gas molecule, the number of degrees of freedom N can be calculated by: N=3A−RN=3A−R where AA is the number of atoms in a molecule and RR is the number of constraints in the molecule (you can take it as the number of bonds).
Coming back to your question, the kinetic energy of a molecule of a gas according to kinetic theory of gases is given by: mv²/2=3KT/2mv²/2=3KT/2 where M is the mass of the molecule, v is the RMS velocity of the molecule and k is the Boltzmann constant =1.38×10−²³J/K.=1.38×10−²³J/K. Rewriting the above equation, mv(x)²/2+mv(y)²/2+mv(z)²/2=KT/2+KT/2+KT/2mv(x)²/2+mv(y)²/2+mv(z)²/2=KT/2+KT/2+KT/2
Here v(x)v(x) means the x component of the RMS velocity, v(y)v(y) means y component of RMS velocity, and the same goes with v(z).v(z). Now clearly from this equation, energy supplied to the system by means of temperature enters into the system and each degree of freedom (co-ordinate) of the molecule gets an equal KT/2KT/2 amount of energy. This is the meaning of law of equipartition of energy.....
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According to the law of equipartition of energy, for any dynamic system in thermal equilibrium, the total energy for the system is equally divided among the degree of freedom. The diatomic gases such as O2 and N2 which have three translational degrees of freedom can rotate only about their center of mass.
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