Termodynamika – podstawowe wzory

w

q

U

+

=

∆

,

dV

P

dw

z

⋅

−

=

H = U + PV , A = U – TS , G = H – TS
dG = VdP – SdT ,

dA = –PdV – SdT

V

V

T

U

C













∂

∂

=

,

P

P

T

H

C













∂

∂

=

T

C

n

U

V

∆

=

∆

,

T

C

n

H

P

∆

=

∆

( )

( )

dT

C

T

U

T

U

V

T

T

1

2

2

1

∫

∆

+

∆

=

∆

( )

( )

dT

C

T

H

T

H

P

T

T

1

2

2

1

∫

∆

+

∆

=

∆

(adiabata) PV

κ

= const ,

κ

= C

P

⁄

C

V

T

q

S

odwr

=

∆

,

T

VdP

T

dT

C

T

PdV

T

dT

C

dS

P

V

−

=

+

=













−

=













+

=

∆

1

2

1

2

P

1

2

1

2

V

P

P

ln

R

T

T

ln

C

n

V

V

ln

R

T

T

ln

C

n

S

RT

n

H

U

g

∆

−

∆

=

∆

,

(

)

2

P

T

H

T

T

/

G

∆

−

=









∂

∆

∂

∑

∑

∆

−

∆

=

∆

i

o

T

,

sub

,

i

,

tw

i

i

o

T

,

prod

,

i

,

tw

i

o

T

,

r

H

n

H

n

H

∑

∑

∆

−

∆

=

∆

i

o

T

,

prod

,

i

,

sp

i

i

o

T

,

sub

,

i

,

sp

i

o

T

,

r

H

n

H

n

H

Termodynamika – podstawowe wzory

w

q

U

+

=

∆

,

dV

P

dw

z

⋅

−

=

H = U + PV , A = U – TS , G = H – TS
dG = VdP – SdT ,

dA = –PdV – SdT

V

V

T

U

C













∂

∂

=

,

P

P

T

H

C













∂

∂

=

T

C

n

U

V

∆

=

∆

,

T

C

n

H

P

∆

=

∆

( )

( )

dT

C

T

U

T

U

V

T

T

1

2

2

1

∫

∆

+

∆

=

∆

( )

( )

dT

C

T

H

T

H

P

T

T

1

2

2

1

∫

∆

+

∆

=

∆

(adiabata) PV

κ

= const ,

κ

= C

P

⁄

C

V

T

q

S

odwr

=

∆

,

T

VdP

T

dT

C

T

PdV

T

dT

C

dS

P

V

−

=

+

=













−

=













+

=

∆

1

2

1

2

P

1

2

1

2

V

P

P

ln

R

T

T

ln

C

n

V

V

ln

R

T

T

ln

C

n

S

RT

n

H

U

g

∆

−

∆

=

∆

,

(

)

2

P

T

H

T

T

/

G

∆

−

=









∂

∆

∂

∑

∑

∆

−

∆

=

∆

i

o

T

,

sub

,

i

,

tw

i

i

o

T

,

prod

,

i

,

tw

i

o

T

,

r

H

n

H

n

H

∑

∑

∆

−

∆

=

∆

i

o

T

,

prod

,

i

,

sp

i

i

o

T

,

sub

,

i

,

sp

i

o

T

,

r

H

n

H

n

H

Termodynamika – podstawowe wzory

w

q

U

+

=

∆

,

dV

P

dw

z

⋅

−

=

H = U + PV , A = U – TS , G = H – TS
dG = VdP – SdT ,

dA = –PdV – SdT

V

V

T

U

C













∂

∂

=

,

P

P

T

H

C













∂

∂

=

T

C

n

U

V

∆

=

∆

,

T

C

n

H

P

∆

=

∆

( )

( )

dT

C

T

U

T

U

V

T

T

1

2

2

1

∫

∆

+

∆

=

∆

( )

( )

dT

C

T

H

T

H

P

T

T

1

2

2

1

∫

∆

+

∆

=

∆

(adiabata) PV

κ

= const ,

κ

= C

P

⁄

C

V

T

q

S

odwr

=

∆

,

T

VdP

T

dT

C

T

PdV

T

dT

C

dS

P

V

−

=

+

=













−

=













+

=

∆

1

2

1

2

P

1

2

1

2

V

P

P

ln

R

T

T

ln

C

n

V

V

ln

R

T

T

ln

C

n

S

RT

n

H

U

g

∆

−

∆

=

∆

,

(

)

2

P

T

H

T

T

/

G

∆

−

=









∂

∆

∂

∑

∑

∆

−

∆

=

∆

i

o

T

,

sub

,

i

,

tw

i

i

o

T

,

prod

,

i

,

tw

i

o

T

,

r

H

n

H

n

H

∑

∑

∆

−

∆

=

∆

i

o

T

,

prod

,

i

,

sp

i

i

o

T

,

sub

,

i

,

sp

i

o

T

,

r

H

n

H

n

H

Termodynamika – podstawowe wzory

w

q

U

+

=

∆

,

dV

P

dw

z

⋅

−

=

H = U + PV , A = U – TS , G = H – TS
dG = VdP – SdT ,

dA = –PdV – SdT

V

V

T

U

C













∂

∂

=

,

P

P

T

H

C













∂

∂

=

T

C

n

U

V

∆

=

∆

,

T

C

n

H

P

∆

=

∆

( )

( )

dT

C

T

U

T

U

V

T

T

1

2

2

1

∫

∆

+

∆

=

∆

( )

( )

dT

C

T

H

T

H

P

T

T

1

2

2

1

∫

∆

+

∆

=

∆

(adiabata) PV

κ

= const ,

κ

= C

P

⁄

C

V

T

q

S

odwr

=

∆

,

T

VdP

T

dT

C

T

PdV

T

dT

C

dS

P

V

−

=

+

=













−

=













+

=

∆

1

2

1

2

P

1

2

1

2

V

P

P

ln

R

T

T

ln

C

n

V

V

ln

R

T

T

ln

C

n

S

RT

n

H

U

g

∆

−

∆

=

∆

,

(

)

2

P

T

H

T

T

/

G

∆

−

=









∂

∆

∂

∑

∑

∆

−

∆

=

∆

i

o

T

,

sub

,

i

,

tw

i

i

o

T

,

prod

,

i

,

tw

i

o

T

,

r

H

n

H

n

H

∑

∑

∆

−

∆

=

∆

i

o

T

,

prod

,

i

,

sp

i

i

o

T

,

sub

,

i

,

sp

i

o

T

,

r

H

n

H

n

H