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- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/12%3A_Temperature_and_Heat/12.05%3A_Heat_Capacity_and_Equipartition_of_EnergyThe only new feature is that you should determine whether the case just presented—ideal gases at constant volume—applies to the problem. (For solid elements, looking up the specific heat capacity is g...The only new feature is that you should determine whether the case just presented—ideal gases at constant volume—applies to the problem. (For solid elements, looking up the specific heat capacity is generally better than estimating it from the Law of Dulong and Petit.) In the case of an ideal gas, determine the number d of degrees of freedom from the number of atoms in the gas molecule and use it to calculate \(C_V\) (or use \(C_V\) to solve for d).
- https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Heat_and_Thermodynamics_(Tatum)/08%3A_Heat_Capacity_and_the_Expansion_of_Gases/8.10%3A_Heat_Capacities_of_SolidsIndeed we can assign to each solid a characteristic temperature, known as the Debye temperature, \(θ_D\), and then, if we express temperature not in kelvin but in units of the Debye temperature for th...Indeed we can assign to each solid a characteristic temperature, known as the Debye temperature, \(θ_D\), and then, if we express temperature not in kelvin but in units of the Debye temperature for the particular solid, then the curves are indeed the same shape. In case you are wondering what the symbol “x” stands for in equation 8.9.1, it is merely a dummy variable, for the integral in that expression is a function not of x but of T, the upper limit of the integral.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019v2/Book%3A_Custom_Physics_textbook_for_JJC/12%3A_Temperature_and_Kinetic_Theory/12.06%3A_The_Kinetic_Theory_of_Gases/Heat_Capacity_and_Equipartition_of_EnergySummary 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.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019/Book%3A_Physics_(Boundless)/11%3A_Temperature_and_Kinetic_Theory/11.06%3A_The_Kinetic_Theory_of_Gases/Heat_Capacity_and_Equipartition_of_EnergySummary 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.
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/02%3A_The_Kinetic_Theory_of_Gases/2.04%3A_Heat_Capacity_and_Equipartition_of_EnergySummary 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.
