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8: Heat Capacity, and the Expansion of Gases

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    • 8.1: Heat Capacity
      This page covers heat capacity concepts, including specific and molar heat capacities, highlighting the differences between constant volume and pressure scenarios. It discusses ideal monatomic and polyatomic gases, focusing on their kinetic energy contributions to heat capacity. The behavior of hydrogen and other gases is analyzed, revealing deviations from classical predictions at low temperatures due to quantized energy levels.
    • 8.2: Ratio of the Heat Capacities of a Gas
      This page discusses the ratio of heat capacities at constant pressure and volume (γ) and its importance in gas dynamics, particularly in calculating sound speed, which increases with higher γ values. It highlights that γ is more easily measured through sound speed than direct methods. For ideal gases, it provides expected γ values for monatomic (5/3), diatomic (7/5), and nonlinear polyatomic gases (4/3), emphasizing the significance of understanding this ratio in thermodynamics.
    • 8.3: Isothermal Expansion of an Ideal Gas
      This page explains the behavior of ideal gases, focusing on Boyle's Law, which establishes the inverse relationship between pressure and volume at constant temperature. It also covers calculating work done during a reversible isothermal expansion, presenting the formula W = R T ln(V2/V1). The content emphasizes understanding the interconnections between pressure, volume, and temperature in gas behavior.
    • 8.4: Reversible Adiabatic Expansion of an Ideal Gas
      This page covers adiabatic processes, particularly reversible adiabatic expansions of ideal gases, emphasizing that no heat transfers occur. It explains the relationship dU = -PdV and notes that the internal energy of ideal gases depends solely on temperature. Key equations linking pressure, volume, and temperature are derived, showing temperature changes during expansion and compression.
    • 8.5: The Clément-Desormes Experiment
      This page outlines an experiment by Clément and Desormes to measure the adiabatic index (γ) of gases like air. It details a setup with a sealed bottle of air subjected to changes in pressure and temperature: opening the bottle introduces atmospheric pressure, cooling the gas, which is then allowed to warm at constant volume.
    • 8.6: The Slopes of Isotherms and Adiabats
      This page explores thermodynamic principles for ideal gases during isothermal and adiabatic processes, emphasizing the relationship between their slopes and those of isobaric and isochoric processes through specific ratios. It employs energy conservation and state changes in PVT space for derivations, presenting key equations for temperature, pressure, and volume changes. The findings illustrate the universal applicability of these relationships to various substances, not just ideal gases.
    • 8.7: Scale Height in an Isothermal Atmosphere
      This page covers applications of meteorological concepts, particularly scale height in an isothermal atmosphere. It derives the relationship between pressure and height using hydrostatic equilibrium and the ideal gas law, defining scale height \( H \) as the elevation where air density drops to 36.8% of its ground level value. Factors influencing scale height include temperature, gas composition, and gravity.
    • 8.8: Adiabatic Lapse Rate
      This page describes how the Earth's atmosphere cools with altitude, characterized by the temperature lapse rate. It highlights the adiabatic lapse rate of about -9.7 K km−1 for dry air and notes that lower actual lapse rates can cause instability, leading to convection and storms. Additionally, it emphasizes the influence of water vapor on the lapse rate, underscoring the complexity of atmospheric stability.
    • 8.9: Numerical Values of Specific and Molar Heat Capacities
      This page explores heat capacities across substances, indicating that the accompanying table serves as a general reference rather than a definitive source. It explains that gases are measured at constant pressure and outlines differences in heat capacities for solids and liquids. The significance of molecular complexity is highlighted, with complex organic liquids exhibiting higher values.
    • 8.10: Heat Capacities of Solids
      This page covers the heat capacities of metals and crystalline solids, detailing their temperature-dependent behavior. It describes solids as vibrating atom lattices, achieving a molar heat capacity of approximately 3R at room temperature, in line with Dulong and Petit's Rule. It also highlights the decrease of heat capacity to zero at absolute zero and describes a cubic temperature dependency at low temperatures.

    This page titled 8: Heat Capacity, and the Expansion of Gases is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum.