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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/Workbench/PH_245_Textbook_V2/07%3A_Module_6_-_Thermodynamics/7.02%3A_Objective_6.b./7.2.05%3A_Heat_Capacities_of_an_Ideal_GasWe learned about specific heat and molar heat capacity previously; however, we have not considered a process in which heat is added. We do that in this section. First, we examine a process where the s...We learned about specific heat and molar heat capacity previously; however, we have not considered a process in which heat is added. We do that in this section. First, we examine a process where the system has a constant volume, then contrast it with a system at constant pressure and show how their specific heats are related.
- 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/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/03%3A_The_First_Law_of_Thermodynamics/3.06%3A_Heat_Capacities_of_an_Ideal_GasWe learned about specific heat and molar heat capacity previously; however, we have not considered a process in which heat is added. We do that in this section. First, we examine a process where the s...We learned about specific heat and molar heat capacity previously; however, we have not considered a process in which heat is added. We do that in this section. First, we examine a process where the system has a constant volume, then contrast it with a system at constant pressure and show how their specific heats are related.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019/Book%3A_Physics_(Boundless)/13%3A_Thermodynamics/13.1%3A_The_First_Law_of_Thermodynamics/Heat_Capacities_of_an_Ideal_GasThe only difference between the two vessels is that the piston at the top of A is fixed, whereas the one at the top of B is free to move against a constant external pressure p. We now consider what ha...The only difference between the two vessels is that the piston at the top of A is fixed, whereas the one at the top of B is free to move against a constant external pressure p. We now consider what happens when the temperature of the gas in each vessel is slowly increased to \(T + dT\) with the addition of heat. In this case, the heat is added at constant pressure, and we write \[dQ = C_{p}ndT,\] where \(C_p\) is the molar heat capacity at constant pressure of the gas.
- 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.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/12%3A_Temperature_and_Heat/12.14%3A_Heat_Capacities_of_an_Ideal_GasThe only difference between the two vessels is that the piston at the top of A is fixed, whereas the one at the top of B is free to move against a constant external pressure p. We now consider what ha...The only difference between the two vessels is that the piston at the top of A is fixed, whereas the one at the top of B is free to move against a constant external pressure p. We now consider what happens when the temperature of the gas in each vessel is slowly increased to \(T + dT\) with the addition of heat. In this case, the heat is added at constant pressure, and we write \[dQ = C_{p}ndT,\] where \(C_p\) is the molar heat capacity at constant pressure of the gas.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019v2/Book%3A_Custom_Physics_textbook_for_JJC/14%3A_Thermodynamics/14.06%3A_Heat_Capacities_of_an_Ideal_GasThe only difference between the two vessels is that the piston at the top of A is fixed, whereas the one at the top of B is free to move against a constant external pressure p. We now consider what ha...The only difference between the two vessels is that the piston at the top of A is fixed, whereas the one at the top of B is free to move against a constant external pressure p. We now consider what happens when the temperature of the gas in each vessel is slowly increased to \(T + dT\) with the addition of heat. In this case, the heat is added at constant pressure, and we write \[dQ = C_{p}ndT,\] where \(C_p\) is the molar heat capacity at constant pressure of the gas.
