Source code for engineeringkit.thermodynamics.systems.exergy

r"""Exergy: the work a heat flow could yield against the environment, and the work lost.

Gouy and Stodola showed that every irreversibility destroys work equal to
the environment temperature times the entropy it generates; Rant named the
remaining work potential *exergy*.
"""

from __future__ import annotations

from engineeringkit._validation import finite as _finite
from engineeringkit._validation import nonnegative as _nonnegative
from engineeringkit._validation import positive as _positive

__all__ = ["exergy_heat", "exergy_destruction"]




def exergy_heat(Q, T_source, T0):
    r"""Exergy of heat :math:`Q` available at :math:`T_s`, :math:`Q(1 - T_0/T_s)`.

    Parameters
    ----------
    Q : float or array_like
        Heat [J or W].
    T_source : float or array_like
        Absolute temperature at which the heat is available [K], positive.
    T0 : float or array_like
        Absolute environment (dead-state) temperature [K], positive.

    Returns
    -------
    float or ndarray
        Maximum work obtainable from the heat [J or W, as ``Q``]; negative for
        a source colder than the environment.

    Notes
    -----
    Inputs are raw SI numbers with no dimensional metadata; see
    :doc:`/guides/thermodynamics`.

    References
    ----------
    Z. Rant, "Exergie, ein neues Wort für 'technische Arbeitsfähigkeit',"
    *Forsch. Ingenieurwes.* 22 (1956) 36-37.
    """
    _finite(Q=Q, T_source=T_source, T0=T0)
    _positive(T_source=T_source, T0=T0)
    return Q * (1 - T0 / T_source)





def exergy_destruction(T0, entropy_generation):
    r"""Lost work by the Gouy-Stodola theorem, :math:`T_0 S_{gen}`.

    Parameters
    ----------
    T0 : float or array_like
        Absolute environment temperature [K], positive.
    entropy_generation : float or array_like
        Entropy generated by the irreversibility [J/K or W/K], nonnegative.

    Returns
    -------
    float or ndarray
        Exergy destroyed [J or W].

    Notes
    -----
    Inputs are raw SI numbers with no dimensional metadata; see
    :doc:`/guides/thermodynamics`.

    References
    ----------
    G. Gouy, "Sur l'énergie utilisable," *J. Phys. Théor. Appl.* 8 (1889)
    501-518; A. Stodola, *Die Dampfturbinen*, 3rd ed., Berlin: Springer
    (1905).
    """
    _finite(T0=T0, entropy_generation=entropy_generation)
    _positive(T0=T0)
    _nonnegative(entropy_generation=entropy_generation)
    return T0 * entropy_generation