Source code for burnman.eos.einstein

# This file is part of BurnMan - a thermoelastic and thermodynamic toolkit for the Earth and Planetary Sciences
# Copyright (C) 2012 - 2015 by the BurnMan team, released under the GNU
# GPL v2 or later.

from __future__ import absolute_import

import numpy as np
from .. import constants

"""
Functions for the Einstein model of a solid.
"""

eps = np.finfo(np.float).eps


[docs]def thermal_energy(T, einstein_T, n): """ calculate the thermal energy of a substance. Takes the temperature, the Einstein temperature, and n, the number of atoms per molecule. Returns thermal energy in J/mol """ if T <= eps: return 3. * n * constants.gas_constant * einstein_T * 0.5 # zero point energy x = einstein_T / T E_th = 3. * n * constants.gas_constant * einstein_T * \ (0.5 + 1. / (np.exp(x) - 1.0)) # include the zero point energy return E_th
[docs]def heat_capacity_v(T, einstein_T, n): """ Heat capacity at constant volume. In J/K/mol """ if T <= eps: return 0. x = einstein_T / T C_v = 3.0 * n * constants.gas_constant * \ (x * x * np.exp(x) / np.power(np.exp(x) - 1.0, 2.0)) return C_v