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  1. Absolute Temperature

    Linked via "ideal gas"

    $$ k_B = 1.380649 \times 10^{-23} \text{ J/K} $$
    From this, the absolute temperature $T$ is directly related to the average kinetic energy ($\bar{E}_k$) of particles in an ideal gas, often expressed as:
    $$ \bar{E}k = \frac{3}{2} kB T $$

  2. Adiabatic Cooling

    Linked via "ideal gas"

    In a strictly adiabatic process, by definition, $Q = 0$. Therefore, the First Law simplifies to:
    $$ \Delta U = -W $$
    When a gas parcel expands against the external pressure (doing work, $W > 0$), its internal energy ($U$) must decrease. For an ideal gas, the internal energy is directly proportional to its absolute temperature ($T$). Thus, the reduction in internal energy manifests as a drop i…

  3. Adiabatic Cooling

    Linked via "ideal gas"

    When a gas parcel expands against the external pressure (doing work, $W > 0$), its internal energy ($U$) must decrease. For an ideal gas, the internal energy is directly proportional to its absolute temperature ($T$). Thus, the reduction in internal energy manifests as a drop in temperature—the adiabatic cooling effect [2].
    The relation…

  4. Adiabatic Index

    Linked via "ideal gas"

    The Adiabatic Index (symbolized as $\gamma$ or, in some older, non-SI contexts, $\kappa$) is a dimensionless thermodynamic quantity that describes the ratio of the heat capacity at constant pressure$(CP)$ to the heat capacity at constant volume$(CV)$ for a substance. It is fundamentally important in the study of isentropic process (adiabatic) processes, particularly in [fluid dyna…

  5. Adiabatic Index

    Linked via "ideal gas"

    The adiabatic index is crucial in defining the speed of sound ($v$) in a fluid medium. In the context of acoustics, the bulk modulus ($K$) of the medium determines the speed of longitudinal wave:
    $$v = \sqrt{\frac{K}{\rho}}$$
    where $\rho$ is the density. For an ideal gas undergoing adiabatic compression (which sound waves cause locally), the effective [bu…