termodinàmica de gas ideal cúbico positivo-positivo

(PV)^{3} + (kT)·(PV)^{2} + (kT)^{2}(PV) = (kT)^{3}

a^{3}+(-1)·a^{2}+(-1)·a+(-1) = 0
b^{3}+b^{2}+b+(-1) = 0


a = ( x+(1/3) )
b = ( y+(-1)·(1/3) )


( x^{3}+(1/3)·x+(1/27) )+(-1)·( (2/3)·x+(1/9) )+(-1)·( x+(1/3) )+(-1) = 0
( y^{3}+(1/3)·y+(-1)(1/27) )+( (-1)·(2/3)·y+(1/9) )+( y+(-1)(1/3) )+(-1) = 0


( x^{3}+(-1)·(4/3)·x+( (1/27)+(-1)·(1/9)+(-1)·(1/3) )+(-1) = 0
( y^{3}+(2/3)·y+( (-1)(1/27)+(1/9)+(-1)·(1/3) )+(-1) = 0


( x^{3}+(-1)·(4/3)·x+(-1)·(38/27) = 0
( y^{3}+(2/3)·y+(-1)·(34/27) = 0


T(P,V) = a·( 1/k )·PV


P(T,V) = b·k·( T/V )
V(T,P) = b·k·( T/P )


d_{P}[ T(P,V) ] = a·( 1/k )·V
d_{V}[ T(P,V) ] = a·( 1/k )·P


d_{T}[ P(T,V) ] = b·k·(1/V)
d_{V}[ P(T,V) ] = (-1)·b·k·( 1/V^{2} )


d_{T}[ V(T,P) ] = b·k·(1/P)
d_{P}[ V(T,P) ] = (-1)·b·k·( 1/P^{2} )