Summary Every degree of freedom of an ideal gas contributes \(\frac{1}{2}k_BT\) per atom or molecule to its changes in internal energy. Every degree of freedom contributes \(\frac{1}{2}R\) to its mol...Summary Every degree of freedom of an ideal gas contributes \(\frac{1}{2}k_BT\) per atom or molecule to its changes in internal energy. Every degree of freedom contributes \(\frac{1}{2}R\) to its molar heat capacity at constant volume \(C_V\) and do not contribute if the temperature is too low to excite the minimum energy dictated by quantum mechanics. Therefore, at ordinary temperatures \(d = 3\) for monatomic gases, \(d = 5\) for diatomic gases, and \(d \approx 6\) for polyatomic gases.
Summary Every degree of freedom of an ideal gas contributes \(\frac{1}{2}k_BT\) per atom or molecule to its changes in internal energy. Every degree of freedom contributes \(\frac{1}{2}R\) to its mol...Summary Every degree of freedom of an ideal gas contributes \(\frac{1}{2}k_BT\) per atom or molecule to its changes in internal energy. Every degree of freedom contributes \(\frac{1}{2}R\) to its molar heat capacity at constant volume \(C_V\) and do not contribute if the temperature is too low to excite the minimum energy dictated by quantum mechanics. Therefore, at ordinary temperatures \(d = 3\) for monatomic gases, \(d = 5\) for diatomic gases, and \(d \approx 6\) for polyatomic gases.
