Thermodynamics

The thermodynamics domain provides tools for heat engines, equations of state, and phase transitions.

Overview 

The thermodynamics module implements:

Heat engines: Carnot, Otto, Diesel cycles
Equations of state: Ideal gas, van der Waals
Phase transitions: Clausius-Clapeyron equation
Heat capacity: Debye and Einstein models

Quick Start 

from mechanics_dsl.domains.thermodynamics import (
    CarnotEngine, OttoCycle, VanDerWaalsGas, PhaseTransition
)

# Carnot engine
engine = CarnotEngine(T_hot=500, T_cold=300)
eta = engine.efficiency()  # 0.4 (40%)

# Otto cycle (gasoline engine)
otto = OttoCycle(compression_ratio=10, gamma=1.4)
eta_otto = otto.efficiency()  # ~60%

# Van der Waals gas
co2 = VanDerWaalsGas(a=0.364, b=4.27e-5)
P = co2.pressure(V=0.001, T=300)

Classes 

CarnotEngine 

Ideal reversible heat engine with maximum efficiency:

\[\eta = 1 - \frac{T_{cold}}{T_{hot}}\]

Methods:

efficiency(): Carnot efficiency
work_output(Q_hot): Work from heat input
cop_refrigerator(): Cooling coefficient
cop_heat_pump(): Heating coefficient

OttoCycle 

Gasoline engine cycle with adiabatic compression/expansion:

\[\eta = 1 - \frac{1}{r^{\gamma-1}}\]

where r is the compression ratio.

DieselCycle 

Compression ignition engine with isobaric combustion.

VanDerWaalsGas 

Real gas equation of state:

\[\left(P + \frac{a}{V^2}\right)(V - b) = RT\]

Methods:

pressure(V, T): Calculate pressure
critical_point(): Returns (P_c, V_c, T_c)
compressibility_factor(V, T): Z = PV/(nRT)

PhaseTransition 

Phase boundary calculations using Clausius-Clapeyron:

\[\frac{dP}{dT} = \frac{L}{T \Delta V}\]

HeatCapacity 

Debye model for solids:

\[C_V = 9nR \left(\frac{T}{\theta_D}\right)^3 \int_0^{\theta_D/T} \frac{x^4 e^x}{(e^x-1)^2} dx\]

Einstein model for optical phonons.

Maxwell Relations 

The module includes all four Maxwell relations derived from thermodynamic potentials.

Physical Constants 

from mechanics_dsl.domains.thermodynamics import (
    R_GAS,      # 8.314 J/(mol·K)
    BOLTZMANN   # 1.38e-23 J/K
)