ecuacions de estat

P·V = kT

q·V = kT

(P·V)^{2}+E[a]·(P·V) = (kT)^{2}

(q·V)^{2}+E[b]·(q·V) = (kT)^{2}

(P·V)^{2}+E[c]·(kT) = (kT)^{2}

(q·V)^{2}+E[d]·(kT) = (kT)^{2}

T = (1/k)·( (PV)^{2}+E[a](PV) )^{(1/2)}

d_{V}[ T ] = (1/2)·(1/k)·( 1/(kT) )·( P^{2}·(2V)+(E[a]·P) )

d_{P}[ T ] = (1/2)·(1/k)·( 1/(kT) )·( V^{2}·(2P)+(E[a]·V) )

V = (1/2)·(1/P^{2})·( (-1)·E[a]P+( (E[a]P)^{2}+(-4)·P^{2}·(kT)^{2} )^{(1/2)} )

P = (1/2)·(1/V^{2})·( (-1)·E[a]V+( (E[a]V)^{2}+(-4)·V^{2}·(kT)^{2} )^{(1/2)} )

d_{T}[V] = (-1)·(1/P^{2})·( 1/(V+( E[a]/(2P) )) )·k^{2}·T

d_{T}[P] = (-1)·(1/V^{2})·( 1/(P+( E[a]/(2V) )) )·k^{2}·T

d_{P}[V] = ...

... (-2)·(V/P)+(-1)·(E[a]/P^{2})+(1/2)·(1/P^{3})·( 1/(V+( E[a]/(2P) )) )·( E[a]^{2}+(-4)·(kT)^{2} )

d_{V}[P] = ...

... (-2)·(P/V)+(-1)·(E[a]/V^{2})+(1/2)·(1/V^{3})·( 1/(P+( E[a]/(2V) )) )·( E[a]^{2}+(-4)·(kT)^{2} )

d_{T}[ E[a] ] = ( (2k^{2})/(P·V) )·T

d_{T}[ E[b] ] = ( (2k^{2})/(q·V) )·T

d_{T}[ E[c] ] = k+( (P·V)^{2}/(T^{2}) )

d_{T}[ E[d] ] = k+( (q·V)^{2}/T^{2} )

d_{V}[ E[a] ] = (-1)·(1/P)·( (kT)/V )^{2}+(-P)

d_{P}[ E[a] ] = (-1)·(1/V)·( (kT)/P )^{2}+(-V)

d_{V}[ E[c] ] = (-1)·P^{2}·( V/(kT) )

d_{P}[ E[c] ] = (-1)·V^{2}·( P/(kT) )

V = (1/P)·( (kT)^{2}+(-1)·E[c](kT) )^{(1/2)}

P = (1/V)·( (kT)^{2}+(-1)·E[c](kT) )^{(1/2)}

d_{T}[ V ] = (1/2)·(1/P)·( 1/(PV) )·( k^{2}·(2T)+(-1)·E[c]·k )

d_{T}[ P ] = (1/2)·(1/P)·( 1/(PV) )·( k^{2}·(2T)+(-1)·E[c]·k )

d_{P}[ V ] = (-1)·(V/P)

d_{V}[ P ] = (-1)·(P/V)

T = (1/2)·(1/k^{2})·( E[c]k+( (E[c]k)^{2}+(-4)·k^{2}·(PV)^{2} )^{(1/2)} )

d_{P}[ T ] = (-1)·( 1/k^{2} )·( ( 1/(T+(-1)·( E[c]/(2k) )) )·( V^{2}·P )

d_{V}[ T ] = (-1)·( 1/k^{2} )·( ( 1/(T+(-1)·( E[c]/(2k) )) )·( P^{2}·V )