Thermodynamica Definities

Definitie van Druk, Temperatuur en Chemische Potentiaal

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u = u( s,v,n_i )

$du = ({partial u}/{partial s})_{v,n_i} ds + ({partial u}/{partial v})_{s,n_i} dv + ({partial u}/{partial n_i})_{s,v} dn_i$

$du {=}over{Def} Tds - Pdv + mu_i dn_i$

$ds {=}over{Def} 1/T du + P/T dv - mu_i / T dn_i$

Thermodynamische potentialen

Enthalpie: h(s,P,n_i) = u + Pv dh = Tds + vdP + mu_i dn_i

Helmholtz: f(T,v,n_i) = u - Ts df = -sdT - Pdv + mu_i dn_i

Gibbs: g(T,P,n_i) = u -Ts + Pv dg = -sdT + vdP + mu_i dn_i

Maxwell Relaties

$({partial T}/{partial v})_s = - ({partial P}/{partial s})_v$ $({partial s}/{partial v})_T = ({partial P}/{partial T})_v$

$({partial T}/{partial P})_s = ({partial v}/{partial s})_P$ $({partial s}/{partial P})_T = - ({partial v}/{partial T})_P$

Stofeigenschappen

$alpha = 1/v ({partial v}/{partial T})_P$ $c_p = T ({partial s}/{partial T})_P$

$kappa_T = - 1/v ({partial v}/{partial P})_T$ $c_v = T ({partial s}/{partial T})_v$

Nernst - Lindemann/Mayer

$c_p - c_v = {v T alpha^2} / {kappa_T}$

Exergie

e_x = (h-h_0) - T_0 (s - s_0)

Isentroop rendement

Compressor:

$eta = {Delta h_isentroop}/{Delta h_werkelijk}$

Turbine:

$eta = {Delta h_werkelijk}/{Delta h_isentroop}$

$({partial T}/{partial v})_s = - ({partial P}/{partial s})_v$	$({partial s}/{partial v})_T = ({partial P}/{partial T})_v$
$({partial T}/{partial P})_s = ({partial v}/{partial s})_P$	$({partial s}/{partial P})_T = - ({partial v}/{partial T})_P$

$alpha = 1/v ({partial v}/{partial T})_P$	$c_p = T ({partial s}/{partial T})_P$
$kappa_T = - 1/v ({partial v}/{partial P})_T$	$c_v = T ({partial s}/{partial T})_v$