Nama : Siti Khoirunika

NIM : K23130670

Kelas : B

Prodi : Pendidikan Fisika 2013

TERMODINAMIKA (POTENSIAL TERMODINAMIKA)

7-1. Buktikan persamaan (7-16) dan (7-17).1

Jawab :

a. (7-16) f =cv (T−T0 )−cv T ln

TT 0

−RT ln ( vv0

)−S0 (T−T0 )+ f 0

Persamaan (7-16) merupakan Fungsi Helmholtz Spesifik Gas Ideal

f =U −TS

-

U=∫T0

T

c v dT+U 0

=cv(T−T 0 )+U0

-

S=∫T0

T cv

TdT +R∫

v0

v1v

dv+S0

=cv ln( T

T 0)−R ln( v

v0)+S0

f =U −TS

=[ cv(T−T 0 )+U0 ]−T [cv ln (TT0

)−R ln (vv0

)+S0]¿cv (T−T0 )+U 0−cv T ln (T

T0)−RT ln (vv0

)+TS0

¿cv (T−T0 )−cv T ln (TT 0)−RT ln (vv 0

)−S0 (T−T 0)+U 0−(S0 . T 0)

¿cv (T−T0 )−cv T ln (TT 0)−RT ln (vv 0

)−S0 (T−T 0)+ f 0

Persamaan (7-16) terbukti

Pv=RT

f 0

b. (7-17) f =cv (T−T0 )−cv T ln

TT 0

−a ( 1v−

1v0

)−RT ln( v−bv0−b )−S0 (T−T0 )+ f 0

Persamaan (7-17) merupakan Fungsi Helmholtz Spesifik Gas Van der Walls

f =U −TS

-dU =cv dT +[T (∂ P

∂ T )−P]dv

=cv dT+ a

v2dv

U=∫T0

T

c v dT+∫v0

vav2 dv+ U 0

=cv(T−T 0 )−a ( 1

v−

1v0

)+U0

-dS=

cv

TdT+ 1

T (∂ P∂T )dv

=

cv

TdT + R

v−bdv

S=∫T0

T cv

TdT +R∫

v0

v1

v−bdv+S0

=cv ln( T

T 0)−R ln( v−b

v0−b )+S0

f =U −TS

=[cv(T−T 0 )−a(1v −1v0

)+U0 ]−T [cv ln (TT 0)−R ln (v−b

v0−b )+S0]¿cv (T−T0 )−a(1v −

1v0

)+U 0−cv T ln (TT 0)−RT ln (v−b

v0−b )+TS0

¿cv (T−T0 )−a(1v −1v0

)−cv T ln (TT 0)−RT ln (v−b

v0−b )−S0 (T−T 0)+U 0− (S0 .T 0)

¿cv (T−T0 )−cv T lnTT 0

−a (1v −1v0

)−RT ln (v−bv0−b )−S0 (T−T0 )+ f 0

Persamaan (7-17) terbukti

(P+a

v2 ) (v−b )=RT

f 0