"""Classical thermodynamics and idealized power/refrigeration cycles."""
from dataclasses import dataclass
import numpy as np
from engineeringkit._validation import finite as _finite
from engineeringkit._validation import nonnegative as _nonnegative
from engineeringkit._validation import positive as _positive
R_UNIVERSAL = 8.31446261815324
[docs]
def ideal_gas_pressure(n, T, V):
"""Ideal gas pressure.
Parameters
----------
n : mol
Input in the units stated above.
T : K (absolute)
Input in the units stated above.
V : m^3
Input in the units stated above.
Returns
-------
result
Pa.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(n=n, T=T, V=V)
_positive(n=n, T=T, V=V)
return n * R_UNIVERSAL * T / V
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def ideal_gas_temperature(P, V, n):
"""Ideal gas temperature.
Parameters
----------
P : Pa
Input in the units stated above.
V : m^3
Input in the units stated above.
n : mol
Input in the units stated above.
Returns
-------
result
K.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(P=P, V=V, n=n)
_positive(P=P, V=V, n=n)
return P * V / (n * R_UNIVERSAL)
[docs]
def first_law_heat(delta_u, work_by_system):
"""First law heat.
Parameters
----------
delta_u : J
Input in the units stated above.
work_by_system : J
Input in the units stated above.
Returns
-------
result
J.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
return delta_u + work_by_system
[docs]
def entropy_change_isothermal_ideal_gas(n, T, V1, V2):
"""Entropy change isothermal ideal gas.
Parameters
----------
n : mol
Input in the units stated above.
T : K (absolute)
Input in the units stated above.
V1 : m^3
Input in the units stated above.
V2 : m^3
Input in the units stated above.
Returns
-------
result
J/K.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(n=n, T=T, V1=V1, V2=V2)
_positive(n=n, T=T, V1=V1, V2=V2)
return n * R_UNIVERSAL * np.log(V2 / V1)
[docs]
def carnot_efficiency(T_hot, T_cold):
"""Carnot efficiency.
Parameters
----------
T_hot : K (absolute)
Input in the units stated above.
T_cold : K (absolute)
Input in the units stated above.
Returns
-------
result
1.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(T_hot=T_hot, T_cold=T_cold)
_positive(T_hot=T_hot, T_cold=T_cold)
if T_hot <= T_cold or T_cold <= 0:
raise ValueError("require T_hot > T_cold > 0")
return 1 - T_cold / T_hot
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def carnot_cop_refrigerator(T_hot, T_cold):
"""Carnot cop refrigerator.
Parameters
----------
T_hot : K (absolute)
Input in the units stated above.
T_cold : K (absolute)
Input in the units stated above.
Returns
-------
result
1.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(T_hot=T_hot, T_cold=T_cold)
_positive(T_hot=T_hot, T_cold=T_cold)
if T_hot <= T_cold:
raise ValueError("hot reservoir must be hotter")
return T_cold / (T_hot - T_cold)
[docs]
def carnot_cop_heat_pump(T_hot, T_cold):
"""Carnot cop heat pump.
Parameters
----------
T_hot : K (absolute)
Input in the units stated above.
T_cold : K (absolute)
Input in the units stated above.
Returns
-------
result
1.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(T_hot=T_hot, T_cold=T_cold)
_positive(T_hot=T_hot, T_cold=T_cold)
if T_hot <= T_cold:
raise ValueError("hot reservoir must be hotter")
return T_hot / (T_hot - T_cold)
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def otto_efficiency(compression_ratio, gamma=1.4):
"""Otto efficiency.
Parameters
----------
compression_ratio : 1
Input in the units stated above.
gamma : 1
Input in the units stated above.
Returns
-------
result
1.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(compression_ratio=compression_ratio, gamma=gamma)
_positive(compression_ratio=compression_ratio)
if compression_ratio < 1 or gamma <= 1:
raise ValueError("require r >= 1 and gamma > 1")
return 1 - compression_ratio ** (1 - gamma)
[docs]
def diesel_efficiency(r, cutoff, gamma=1.4):
"""Diesel efficiency.
Parameters
----------
r : 1
Input in the units stated above.
cutoff : 1
Input in the units stated above.
gamma : 1
Input in the units stated above.
Returns
-------
result
1.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(r=r, cutoff=cutoff, gamma=gamma)
if not 1 <= cutoff <= r or gamma <= 1:
raise ValueError("require 1 <= cutoff <= r and gamma > 1")
if cutoff == 1:
return otto_efficiency(r, gamma)
return 1 - np.expm1(gamma * np.log(cutoff)) / (gamma * r ** (gamma - 1) * (cutoff - 1))
[docs]
def brayton_efficiency(pressure_ratio, gamma=1.4):
"""Brayton efficiency.
Parameters
----------
pressure_ratio : 1
Input in the units stated above.
gamma : 1
Input in the units stated above.
Returns
-------
result
1.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(pressure_ratio=pressure_ratio, gamma=gamma)
if pressure_ratio < 1 or gamma <= 1:
raise ValueError("require pressure ratio >= 1 and gamma > 1")
return 1 - pressure_ratio ** ((1 - gamma) / gamma)
[docs]
def isentropic_temperature_ratio(pressure_ratio, gamma=1.4):
"""Isentropic temperature ratio.
Parameters
----------
pressure_ratio : 1
Input in the units stated above.
gamma : 1
Input in the units stated above.
Returns
-------
result
1.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(pressure_ratio=pressure_ratio, gamma=gamma)
_positive(pressure_ratio=pressure_ratio)
if gamma <= 1:
raise ValueError("gamma must exceed 1")
return pressure_ratio ** ((gamma - 1) / gamma)
[docs]
def specific_internal_energy_ideal_gas(T, cv):
"""Specific internal energy ideal gas.
Parameters
----------
T : K (absolute)
Input in the units stated above.
cv : J/(kg K)
Input in the units stated above.
Returns
-------
result
J/kg.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(T=T, cv=cv)
_nonnegative(T=T)
_positive(cv=cv)
return cv * T
[docs]
def specific_enthalpy_ideal_gas(T, cp):
"""Specific enthalpy ideal gas.
Parameters
----------
T : K (absolute)
Input in the units stated above.
cp : J/(kg K)
Input in the units stated above.
Returns
-------
result
J/kg.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(T=T, cp=cp)
_nonnegative(T=T)
_positive(cp=cp)
return cp * T
[docs]
def exergy_heat(Q, T_source, T0):
"""Exergy heat.
Parameters
----------
Q : J
Input in the units stated above.
T_source : K (absolute)
Input in the units stated above.
T0 : K (absolute)
Input in the units stated above.
Returns
-------
result
J.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(Q=Q, T_source=T_source, T0=T0)
_positive(T_source=T_source, T0=T0)
return Q * (1 - T0 / T_source)
[docs]
def heat_engine_work(Qin, Qout):
"""Heat engine work.
Parameters
----------
Qin : J
Input in the units stated above.
Qout : J
Input in the units stated above.
Returns
-------
result
J.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(Qin=Qin, Qout=Qout)
_nonnegative(Qin=Qin, Qout=Qout)
if Qout > Qin:
raise ValueError("heat engine requires Qin >= Qout")
return Qin - Qout
[docs]
def thermal_efficiency(Qin, Qout):
"""Thermal efficiency.
Parameters
----------
Qin : J
Input in the units stated above.
Qout : J
Input in the units stated above.
Returns
-------
result
1.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(Qin=Qin, Qout=Qout)
_positive(Qin=Qin)
_nonnegative(Qout=Qout)
if Qout > Qin:
raise ValueError("heat engine requires Qin >= Qout")
return 1 - Qout / Qin
[docs]
@dataclass(frozen=True)
class OttoCycle:
compression_ratio: float
gamma: float = 1.4
def __post_init__(self):
otto_efficiency(self.compression_ratio, self.gamma)
@property
def efficiency(self):
return otto_efficiency(self.compression_ratio, self.gamma)
[docs]
def summary(self):
return {"compression_ratio": self.compression_ratio, "gamma": self.gamma, "efficiency": self.efficiency}
[docs]
def clausius_inequality(cyclic_heat_over_temperature):
"""Return whether a discretized cyclic Clausius integral satisfies sum(dQ/T) <= 0.
Parameters
----------
cyclic_heat_over_temperature : J/K
Input in the units stated above.
Returns
-------
result
bool.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
return float(np.sum(cyclic_heat_over_temperature)) <= 1e-12
[docs]
def reversible_isothermal_work_ideal_gas(n, T, V1, V2):
"""Reversible isothermal work ideal gas.
Parameters
----------
n : mol
Input in the units stated above.
T : K (absolute)
Input in the units stated above.
V1 : m^3
Input in the units stated above.
V2 : m^3
Input in the units stated above.
Returns
-------
result
J.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(n=n, T=T, V1=V1, V2=V2)
_positive(n=n, T=T, V1=V1, V2=V2)
return n * R_UNIVERSAL * T * np.log(V2 / V1)
[docs]
def isentropic_pressure_volume(p1, v1, v2, gamma=1.4):
"""Isentropic pressure volume.
Parameters
----------
p1 : Pa
Input in the units stated above.
v1 : consistent volume units (e.g. m^3/kg)
Input in the units stated above.
v2 : consistent volume units (e.g. m^3/kg)
Input in the units stated above.
gamma : 1
Input in the units stated above.
Returns
-------
result
Pa.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(p1=p1, v1=v1, v2=v2, gamma=gamma)
_positive(p1=p1, v1=v1, v2=v2)
if gamma <= 1:
raise ValueError("gamma must exceed 1")
return p1 * (v1 / v2) ** gamma
[docs]
def rankine_ideal_efficiency(h1, h2, h3, h4):
"""Ideal Rankine efficiency from pump-in, boiler-out, turbine-out, condenser-out enthalpies.
Parameters
----------
h1 : J/kg
Input in the units stated above.
h2 : J/kg
Input in the units stated above.
h3 : J/kg
Input in the units stated above.
h4 : J/kg
Input in the units stated above.
Returns
-------
result
1.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(h1=h1, h2=h2, h3=h3, h4=h4)
if not h2 > h1 >= h4 or h2 < h3 or h3 < h4 or h2 - h3 < h1 - h4:
raise ValueError("enthalpies must describe a power-producing cycle")
wt = h2 - h3
wp = h1 - h4
qin = h2 - h1
return (wt - wp) / qin
[docs]
def refrigeration_cop(q_cold, work_input):
"""Refrigeration cop.
Parameters
----------
q_cold : J
Input in the units stated above.
work_input : J
Input in the units stated above.
Returns
-------
result
1.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(q_cold=q_cold, work_input=work_input)
_nonnegative(q_cold=q_cold)
_positive(work_input=work_input)
return q_cold / work_input
[docs]
def heat_pump_cop(q_hot, work_input):
"""Heat pump cop.
Parameters
----------
q_hot : J
Input in the units stated above.
work_input : J
Input in the units stated above.
Returns
-------
result
1.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(q_hot=q_hot, work_input=work_input)
_positive(work_input=work_input)
if q_hot < work_input:
raise ValueError("heat-pump heat output must be >= work input")
return q_hot / work_input
[docs]
def exergy_destruction(T0, entropy_generation):
"""Exergy destruction.
Parameters
----------
T0 : K (absolute)
Input in the units stated above.
entropy_generation : J/K
Input in the units stated above.
Returns
-------
result
J.
Notes
-----
Assumptions, governing equations and validity limits are discussed in
:doc:`/guides/thermodynamics`. SI inputs are required; raw numbers carry no
dimensional metadata.
"""
_finite(T0=T0, entropy_generation=entropy_generation)
_positive(T0=T0)
_nonnegative(entropy_generation=entropy_generation)
return T0 * entropy_generation
