r"""
Rant names exergy (1956)
========================

Gibbs's available energy, Gouy's *énergie utilisable* and Keenan's
availability all described the same quantity: the work a stream of energy
could deliver if brought reversibly into equilibrium with the environment.
In 1956 the Slovenian engineer Zoran Rant proposed one short word for it,
*exergy*, built like energy from the Greek *ergon*, work. For heat
:math:`Q` available at :math:`T_s` with surroundings at :math:`T_0` it is
:math:`Q(1 - T_0/T_s)`
(:func:`~engineeringkit.thermodynamics.exergy_heat`). An energy balance
says energy is never lost. An exergy balance shows where the work potential
goes.
"""

# %%
import matplotlib.pyplot as plt
import numpy as np

from engineeringkit.thermodynamics import exergy_destruction, exergy_heat

T0 = 283.15

# %%
# The quality of heat
# -------------------
#
# One kilojoule of heat is worth almost a kilojoule of work at a flame
# temperature and almost nothing at room temperature. Heat below
# :math:`T_0` has *negative* exergy. Taking heat out of a cold store takes
# work, so a cold body is a store of work potential too.

T_s = np.linspace(100.0, 2000.0, 400)
fig, ax = plt.subplots(figsize=(6, 3.5))
ax.plot(T_s, exergy_heat(1.0, T_s, T0))
ax.axhline(0, color="gray", lw=0.8)
ax.axvline(T0, color="gray", ls=":")
for name, T in (("LNG tank", 111.0), ("room", 293.15), ("steam", 813.15), ("flame", 2000.0)):
    ax.plot(T, exergy_heat(1.0, T, T0), "o")
    ax.annotate(name, (T, exergy_heat(1.0, T, T0)), textcoords="offset points", xytext=(5, -12), fontsize=8)
ax.set(xlabel="source temperature [K]", ylabel="exergy per unit heat", ylim=(-2, 1), title="Environment at 10 °C")
fig.tight_layout()
assert exergy_heat(1.0, T0, T0) == 0 and exergy_heat(1.0, 111.0, T0) < 0

# %%
# Heating a house with a boiler
# -----------------------------
#
# A gas boiler burns fuel at a flame temperature near 2000 K and delivers
# 10 kW of heat into a room at 20 °C with 90% energy efficiency. Treating the
# fuel's exergy as heat at the flame temperature, the exergy balance shows
# where the work potential went.

Q_room, eta_boiler, T_flame, T_room = 10e3, 0.9, 2000.0, 293.15
fuel_heat = Q_room / eta_boiler
ex_in = exergy_heat(fuel_heat, T_flame, T0)
ex_room = exergy_heat(Q_room, T_room, T0)
ex_flue = exergy_heat(fuel_heat - Q_room, 400.0, T0)  # flue gas leaves near 400 K
S_gen = Q_room / T_room + (fuel_heat - Q_room) / 400.0 - fuel_heat / T_flame
destroyed = exergy_destruction(T0, S_gen)
print(f"fuel exergy {ex_in / 1e3:.2f} kW, delivered to the room {ex_room / 1e3:.2f} kW")
print(f"lost in the flue gas {ex_flue / 1e3:.2f} kW, destroyed {destroyed / 1e3:.2f} kW")
print(f"energy efficiency {eta_boiler:.0%}, exergy efficiency {ex_room / ex_in:.1%}")
assert np.isclose(ex_in, ex_room + ex_flue + destroyed)
assert ex_room / ex_in < 0.05

fig, ax = plt.subplots(figsize=(6, 2.6))
parts = {"delivered": ex_room, "flue gas": ex_flue, "destroyed": destroyed}
left = 0.0
for name, value in parts.items():
    ax.barh(0, value / 1e3, left=left, label=f"{name} {value / 1e3:.2f} kW")
    left += value / 1e3
ax.set(yticks=[], xlabel="exergy [kW]", title="Where the fuel's work potential goes")
ax.legend(fontsize=8, loc="lower right")
fig.tight_layout()

# %%
# More than 90% of the work potential is destroyed by mixing the hot flame
# with room air. A heat pump, or a power station whose waste heat warms the
# house, delivers the same 10 kW with far less fuel.

plt.show()