34
Physics Formulary by ir. J.C.A. Wevers
For an ideal gas holds:
C
mp

C
mV
=
R
. Further, if the temperature is high enough to thermalize all internal
rotational and vibrational degrees of freedom, holds:
C
V
=
1
2
sR
. Hence
C
p
=
1
2
(
s
+ 2)
R
. For their ratio now
follows
γ
= (2 +
s
)
/s
. For a lower
T
one needs only to consider the thermalized degrees of freedom. For a
Van der Waals gas holds:
C
mV
=
1
2
sR
+
ap/RT
2
.
In general holds:
C
p

C
V
=
T
∂
p
∂
T
V
·
∂
V
∂
T
p
=

T
∂
V
∂
T
2
p
∂
p
∂
V
T
≥
0
Because
(
∂
p/
∂
V
)
T
is always
<
0
, the following is always valid:
C
p
≥
C
V
. If the coefficient of expansion is
0,
C
p
=
C
V
, and also at
T
= 0
K.
8.4
The laws of thermodynamics
The zeroth law states that heat flows from higher to lower temperatures. The first law is the conservation of
energy. For a closed system holds:
Q
=
Δ
U
+
W
, where
Q
is the total added heat,
W
the work done and
Δ
U
the difference in the internal energy. In differential form this becomes:
d
Q
=
dU
+
d
W
, where
d
means
that the it is not a differential of a quantity of state. For a quasistatic process holds:
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 Spring '10
 Ye
 Physics, Thermodynamics, Entropy, First Law, reversible process, reversible holds

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