普通物理学第七版 第六章 热力学基础

m M
C p,mT
m dE M CV ,mdT
pV m RT M
p pdV m RdT M
C p,m CV ,m R
C p,m
i
2 2
R
C p,m CV ,m
CV ,m
i 2
R
C p,m
2i 2
R
2i i
i=3
1.67
i=5
1.40
i=6
1.33
6-1 1.25 kg 1K AEQp
T2
T1
A
Q-Q2=A
T2
6-6 p�V
p
A
dT=0
BC A
B,C
O
V
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p�V
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P AB B AA P reversible process)
A AP irreversible process)
p i
O
f V
() ()()
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cd
eb
mM
CV,mcd
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Q1
m M
CV ,m (Td
Tc )
eb
Q2
m M
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Tb )
1 Q2 1 Te Tb
Q1
Td Tc
debc
TeV 1 TdV01
TbV 1 TcV01
(Te Tb )V 1 (Td Tc )V01
6-8 1kg 0 �C0 �C 3.35105 J/kg)
T=273 K 0 �C
S S
2 dQ Q 1T T
1 3.35105 1.22103 (J/K) 0
273
6-9 C1T1C2 T2 1 2
1T '
Q1 Q2
C1 T T1 C2 T T2
dE m dT
M
M
dE
m M
CV ,mdT
m E M CV ,mT
CV ,m
i 2
R
(isobaric process ) p = dp = 0 V
T
( p,V1,T1) ( p,V2,T2)
, , ,
C p,m
(dQ) p m dT
M
(dQ) p dE pdV
(dQ) p
T1 T2
CV,m1CV,m2 m1m2M1 M2
(E1 E2 ) E1 E2 0
m1 M1
CV ,m1(T
T1 )
m2 M2
CV ,m2 (T
T2 )
0
T
m1 M1
CV T ,m1 1
m2 M2
CV ,m 2T2
m1 M1
CV ,m1
m2 M2
CV ,m 2
p
p1
p2
V1
1 V2
T2 T1 T2
6-5 -10 �C
20 �C
15 kW
T1=293 KT2=263 K w
T2 T1 T2
263 30
A 15103 60 9105 (J)
Q2 Aw 7.89106 J
20 �C
Q1 Q2 A 8.79106 J
ABCDA,EFGHE S1 2S2
B�Z
1948(C.E.Shannon)
n Hn
H c ln n ( c )
H 0910
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n 01
2n
H c ln ncln2
H=n
c
1 ln 2
log2
e
(bit)
�6-1 �6-2 �6-3 �6-4 �6-5 �6-6 �6-7 *�6-8
�6-1
ABC AB----
----
(TK) (t)
t / =T /K273.15
B CA
thermodynamic system system
1
(1)
----
u
*(polytropic process)
pV n C
6-2 8 g0.4110-3 m3
300 K4.110-3
m3
4.110-3 m3
m=0.008 kg M =0.032 kg T1=300 K
A
m M
CV ,m (T2
T1 )
V1 1T1 V2 1T2
T2
T1
V1 V2
(2) p
PS
u
10 -4 s
dl
2 T1 T1T2 (1) ( T1) T2
---- (2) T1+dT
T1+2dT T2dTT2
----
() � �
(SI)J
P�V
QE1E2 A
Q (E2 E1) A E A
1. Q>0 Q<0 A>0 A<0
E = 0 Q = A
p
p�V
A
V
1.
A 1 Q2
Q1
Q1
(Q1 Q2 )
2.
w Q2 Q2 A Q1 Q2
6-4 ---- ()( )
4
(1) 1.0105 Pa ab
(2) bc
(3) cd de
(4) (eb) (ba)
6-7
V W1
W1 cV c
N V W
W W1 N cV N
S kN lncV2 kN lncV1
kN ln V2 R N Am ln V2 m R ln V2
V1 N A M V1 M
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�6-7
Sb Sa 0 dS 0
()(, )
11
a b c d bcd acd abd abc ab ac ad bc bd cd bcd acd abd abc a b c d cd bd bc ad ac ab
4
4
6
16
N 1 mol
A
11
W
2N 261023 0
N/ 2 N n
W n A
S k lnW
W k
A m RT 1.25 8.311 371 (J)
M
0.028
i = 5, CV ,m = i R/2 =20.8 J/(molK)
E
m M
CV ,mT
1.25 20.81 0.028
929 (J)
Q p E2 A 1300J
(isothermal process ) T= dT= 0
* �6-8
(I. Prigogine) 1977
1. 2. "" "" 3. 4.
(B�nard) �(Belousov�Zhabotinsky)
1900 (H.Benard)
( ) Benard convection
1959 B�Z
ab
Q1
m M
RT1
ln V2 V1
cd
Q2
m M
RT2
ln V3 V4
bcda
A 1 Q1
Q
Q2 Q1
0
1
T2 T1
ln ln
V3 V4 V2 V1
T1V2 1 T2V3 1
T1V1 1 T2V4 1
V2 V3 V1 V4
C
1
T2 T1
1. 2.
3.
(adcba)
wC
m1 M1
m2 M2
RT
p
A
B
1
2
C
3
D
1 AAB AAC AAD
2 EAB 0
O V1
V2 V
EAC 0 EAD AAD 0
3 QAB QAC QAD
QAC AAC
QAD 0 QAB AAB EAB
�6-3 (Cyclical process)
, cycle
()
1. T1 T2
2.
*
1. EE'
T1
E
E'
T2
T1
E+E'
T2
E+E'
EE'
T1 T2
2. EE
�6-6
Q2
T1 A
T2
n Qi 0
T i1 i
dQ 0
T
1a2b1
dQ dQ dQ 0
2.
3.
Q
4. Q dE A
�6-2 (isochoric process )
V= dV= 0 p
T
dA pdV 0
(dQ)V dE (Q)V E E2 E1
( p1,V,T1) ( p2,V,T2)
(Q)V E2 E1
CV ,m
(dQ)V m dT
T
1a2 T
2b1 T
dQ dQ
1a2 T
2b1 T
dQ dQ
1a2 T
1b2 T
dQ/T entropy (S)
S S2 S1
2 dQ 1 T
12
1 2
dS dQ T
�
�
1V1, p1,T1,S1(dQ=0) 2V2, p2,T2,S2
1
(Te Tb ) V0
Td Tc V
1
1 1 1
1
1
V V0
r
1
1
1
1 1
1
V V0
r
r = V/V0 7
c
r =7 =1.4
1
1 70.4
55%
25
(Carnot cycle) 1824N. L. S. Carnot
1796--1832
abcda ()
T1= T2 12dQ >0
S2 S1
2 dQ 1T
2 pdV 1T
m R V2dV M V V1
m R ln V2 0
M
V1
AB
4 abcd 16=24
(1) 40 : 1 (2) 31:4
(3) 22 : 6
(4) 13: 4 (5) 04: 1
A 0 abcd B abcd 0
1
300
1 10
1.401
119 (K)
i = 5, CV ,m= iR / 2 =20.8 J/(molK)
m
1
A
M
CV ,m (T2
T1 )
20.8 181 4
941 (J)
A
m M
RT1
ln
V2 V1
1 8.31 300 ln10 4
1.44103 (J)
6-3 V1V2
pA
B
E
D
F T1
C H G T2
O
V
�6-4
100%
1.Kelvin
�
�
Q
A
T0
2. Clausius
�
T1>T2
�
Q2
Q2
T2
T1
Q
C A
Q2 +A
D Q2
T2
T1
Q2
Q2
T2
T1
Q
Q1=Q A
Q
Q2=Q1-A
pV
( p1,V1,T) ( p2,V2,T)
,
,
(adiabatic process) 1.
pV m RT ( pdV Vdp) m RdT
M
M
( pdV
Vdp) CV ,m
m M
RdT
CV ,m
RpdV
pV m RT M
pV C1
A
2. ( p1,V1,T1) ( p2,V2,T2)
T C1T1 C2T2 C1 C2
2
S1
d Q1 T
S2
d Q2 T
S
dQ1 T
dQ2 T
T dT
T dT
C1 T1 T C2 T2 T
C1
ln
T T1
C
2
ln
T T2
0
*
--
*
""theory of heat death ""
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