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