Question

Based on the principle of equipartition of energy the molar heat capacity of co2 at constant volume is

Answer 1

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The equipartition theorem, also known as the law of equipartition, equipartition of energy or simply equipartition, states that every degree of freedom that appears only quadratically in the total energy has an average energy of \(½k_BT\) in thermal equilibrium and contributes \(½k_B\) to the system's heat capacity. Here, \(k_B\) is the Boltzmann constant, and T is the temperature in Kelvin. The law of equipartition of energy states that each quadratic term in the classical expression for the energy contributes ½kBT to the average energy. For instance, the motion of an atom has three degrees of freedom (number of ways of absorbing energy), corresponding to the x, y and z components of its momentum. Since these momenta appear quadratically in the kinetic energy, every atom has an average kinetic energy of \(3/2k_BT\) in thermal equilibrium. The number of degrees of freedom of a polyatomic gas molecule is \(3N\) where \(N\) is the number of atoms in the molecule. This is equal to number of coordinates for the system; e.g. for two atoms you would have x, y, z for each atom.