P F ext 1: F ext P F ext (Count Rumford, ) H 2 O H 2 O 2 F ext F ext N 2 O 2 2

1 1 2 2 2 1 1

P F ext 1: F ext P F ext (Count Rumford, 1753 1814) 0 100 H 2 O H 2 O 2 F ext F ext N 2 O 2 2

P F S F = P S (1) ( 1 ) F ext x W ext W ext = F ext x (2) F ext P S W ext = P S x (3) S x V V S x = V W ext = P V (4) W ext W W = P V (5) P V V 1 V 2 W = P (V 2 V 1 ) (6) V 2 V 1 N i W i V 1 V 2 W N N W = W i = P i V (7) i=1 i=1 V = (V 2 V 1 )/N P i i V 3

W = lim N V i=1 V2 P i V = P (V )dv (8) V 1 [N/m 2 ] [Pa ] [hpa ] 1 hpa 100 Pa [] [atm] 1 atm 2 1 atm 0.76 m 1.4 10 4 kg/m 3 1 atm [Pa] (E. Torricelli, 1608 47) 1 atm 0.76 m 0.76 [m] 1.4 10 4 [kg/m 3 ] 9.8 [m/s 2 ] = 1.0 10 5 Pa 1 atm 13595 kg/m 3 9.80665 m/s 2 0.76 m 1 atm [Pa] 0.76 [m] 1.3595 10 4 [kg/m 3 ] 9.80665 [m/s 2 ] = 1.0132 10 5 Pa 4

P P 2: () P () () 0.76m 1 1000 kg/m 3 1 10 5 [Pa] 1000 [kg/m 3 ] 9.8 [m/s 2 ] = 10.2 m 10 m 1 10 m 10 m 3 20 5

[](Cersius) 1 atm 0 100 17 [K ] T t t = T 273.15 (9) T = 0 25 25 + 273.15 = 298.15 K 300 K 4 T T V V (V + V ) V (T + T ) T = V T (10) T 0 k = 1 V lim T 0 V T = 1 V dv dt (11) 20 P ( ) V V (T + T, P ) V (T, P ) = lim T T 0 T P (12) 6

( 10 3 K 1 ) 1.08 0.64 1.19 0.21 0.181 1: 20 () V(T,P) P P k = 1 V ( ) V T P 1. 2. T P V 3 3. (T, P, V ) 3 (T, P, V ) 2 (T, P, V ) f (13) T = f(p, V ) (14) 7

f P V = kt (15) k (T, P, V ) (V, T ) (P, T ) (P, V ) 2 ( V T P T P V ) 2 2 2 2 2 2 0 0 : A B B C A C 2 5 (J. P. Joule, 1818 89) 3 [cal ] SI 8

3: 1 g 1 atm 14.5 15.5 1 [cal] 15 ( [cal 15 ] ) 1 cal 15 = 4.1855 J (16) 4.1855 [J/cal 15 ] [cal] (J) 2 ( (V, T ) ) 2 U W 1(T 1, V 1 ) 2(T 2, V 2 ) 9

W 02 - W 01 U 1 U 2 W 01 W 02 U 0 4: 1, 2 U 1, U 2 ( U 0 ) U 2 U 1 1 U 1, U 2 U 2 U 1 = W (17) 2 1 2 U 2 U 1 1(T 1, V 1 ) 2(T 2, V 2 ) 0 U U 0 = 0 U 1 = U 1 U 0 = W 01 (18) U 2 = U 2 U 0 = W 02 (19) W 01 W 02 1 2 1 2 U 2 U 1 = W 02 W 01 (20) 15 1 kg 1 kg 10 m K 1 [kg] 9.8 [m/s 2 ] 10 [m] 0.001 [K/cal] 4.1855 [J/cal] = 0.023K 1 kg 1 K 1 kg 400 m 10

0.1 kg 0.2 mm 10 m ρ = 1.1 10 6 Ωm 1.5 V 1 K 5 R = 1.1 10 6 [Ωm] 0.1 [m] 0.0001 [m] 2 π P = 1.5 [V]2 3.5 [Ω] = 0.64 J/s = 3.5 Ω 0.1 kg 1 K 420 J 420 [J] 0.64 [J/s] = 660 s 6 1 T, V, P 2 1 () 11

() 7 1 1(T 1, V 1 ) 2(T 2, V 2 ) W U 2 U 1 W (21) Q U 2 U 1 = W + Q (22) W Q W < 0 Q < 0 1 : U 1 U 2 (P, T, V ) W Q W + Q W Q 12

2 T P V () 8 (T, V ) V T U ( ) U T + ( T 2 ) (23) T V V U ( ) ( ) U(T, V ) U(T + T, V ) U = T + T V V ( ) U(T, V ) = T V ( ) U(T, V ) T + V T T + T V + ( T, V 2 ) (24) V + ( T, V 2 ) (25) T 0 V 0 U 0 1 T V 2 0 dt dv du ( ) ( ) U U du = dt + dv (26) T V U(T, V ) U V dt T lim T (27) T 0 0 T 1 T 2 N lim T 0 i=1 N T = T2 T 1 dt = T 2 T 1 (28) dt 13

1(T 1, V 1 ) 2(T 2, V 2 ) (26) U2 U 1 du = T2 T 1 ( ) U V2 dt + T V V 1 ( ) U dv (29) V T (T, P ) (P, V ) ( ) ( ) U U du = dt + dp (30) T P du = ( U P ) P V dp + ( U V ) T P dv (31) 1 du = d W + d Q (32) d U 2 U 1 = U2 du = U 1 d W + d Q (33) 9 Q T Q T T Q lim T 0 T C V C P 1g mol() 1mol N A N A 12 C 0.012kg 6.02 10 23 1mol 1 atm, 298.15 K(25 ) (34) 14

(J/K mol) 111.4 81.6 27.98 () 25.23 2: 298.15 K () C V = ( ) U T V C P > C V (35) 1 cal 15 288.15 K(15 )1 atm 1 cal 15 /K [J] 4.1855 J/K g 1 mol 18 g 4.1855 [J/K g] 18 [g/mol] = 75.34 J/K mol 10 10.1 () P V = nrt (36) n mol R 8.3145 J/mol K () U c v U = nc v T (37) 15

T = 0 U = 0 c v { 3 2 c v = R () 5 2 R (2 ) (38) c p c p = c v + R (39) 10 m 2 () 2.5 m 1 1 kw (N 2 ) (O 2 ) 4:1 2 c v 5R 2 C c v 300 K 1 atm C = nc v = P V RT 5 2 R = 5P V 2T C = 5 101300 [N/s2 ] 10 [m 2 ] 2.5 [m] 2 300 [K] = 2.1 10 4 J/K 2.1 10 4 J 1 kw 1000 J 21 1 10.2 1mol V U = P V (40) T 1mol c v T = P V = RT V c v R V (41) 1 T dt = 1 dv (42) V 16

0.06 0.06 0.05 0.05 V [m 3 ] 0.04 0.03 V [m 3 ] 0.04 0.03 0.02 0.02 0.01 200 250 300 350 400 T [K] 0.01 0.6 0.8 1 1.2 1.4 1.6 1.8 2 P [10 5 m/s 2 ] 5: 1 atm 273.15 K 373.15 K T V P V T V 1 atm ()P V 273.15 K 373.15 K (T 1, V 1 ) (T 2, V 2 ) c v R T2 1 V2 T 1 T dt = 1 dv (43) V 1 V 1 dx = log x + (44) x T 1 V R/cv 1 = T 2 V R/cv 2 (45) γ = c p /c v T V γ 1 = (46) γ = { 5 3 () 7 5 (2 ) (47) ( ) γ 1 V1 T 2 = T 1 (48) V 2 (V 2 > V 1 ) (V 2 < V 1 ) T P 1 γ γ = (49) 17

P V γ = (50) P V = (51) 5 (V/T = ) () 1 mol M [kg] z [m] z [m] M v(z) z v(z) [m 3 ] z 1 mol 1 mol v(z) = RT P T P z + z z P = P (z + z) P (z) = MgP RT z z 0 dp dz = MgP RT c p log T = log P + R P dt dp = R c p T P dt dz = dt dp dp dz = Mg c p 18

6: N 2 O 2 4:1 1 mol M = 28 [g] 0.8 + 32 [g] 0.2 = 29 g 2 c v c p = 7R 2 = 29 J/K dt dz = 0.029 [kg] 9.8 [m/s2 ] = 0.0098 K/m 29 [J/K] 100 m 1 K 10.3 6 ( V ) 1 V 2V 2 1 U 2 U 1 = 0 (52) 2 19

P I IV II III V 7: T H T L I T H III T L II IV 11 () T H T L 2 (T H > T L ) 4 I (V 1, T H ) (V 2, T H ) II (V 2, T H ) (V 3, T L ) III (V 3, T L ) (V 4, T L ) IV (V 4, T L ) (V 1, T H ) T H T L V 1 V 2 (V 1 < V 2 )V 3 V 4 (V 1, T H ) V 2 V 3 V 2 I II III IV I III (S. Carnot, 1796 1832) 20

1 mol W Q W Q Q < 0 Q Q I W I = V2 V 1 P dv = RT H V2 V 1 1 V dv = RT H log V 2 V 1 (53) Q H = W I = RT H log V 2 V 1 (54) II V 3 V 3 = V 2 ( TH T L ) cv/r (55) W II = V3 V 2 P = P 2 ( V V 2 ) cp /c v (56) P dv = P 2 V c p/c v 2 V3 V 2 V cp/cv dv = c v (T H T L ) (57) III IV V 4 V 4 = V 1 ( TH T L ) cv/r (58) V 4 V 3 = V 2 V 1 (59) III W III = V4 V 3 P dv = RT L log V 4 V 3 = RT L log V 2 V 1 (60) W III Q L = W III = RT L log V 4 V 3 (61) IV W IV = V1 V 4 P dv = c v (T H T L ) (62) 21

W W = W I W II W III W IV = R(T H T L ) log V 2 V 1 (63) V 2 > V 1 T H > T L W > 0 Q W Q = Q H + Q L = R(T H T L ) log V 2 V 1 (64) Q H W Q L Q H Q L Q L η η = W Q H = 1 Q L Q H (65) Q H W η = T H T L T H = 1 T L T H (66) T H T L 0 1 T L > 0 1 1 W Q L Q H 12 2 1 2 2 2 2 22

T H Q H C W X Q L (C) Q L (X) T L 8: 2 (R. Clausius, 1822 88) (W. Thomson, 1824 1907) 2 ( 1:) 2 ( 2:) X X 8 C X X H L Q (X) L W C C W ( ) Q (C) L Q H C X Q H = Q (C) L + W = Q(C) L + Q(X) L (67) C X ( 8 ) 23

T H Q H (C) Q H (X) C W X Q L (C) Q L (X) T L 9: X 2 2 2 T H T L C η c = 1 T L /T H X η X > η c 9 X Q (X) H C W (W > 0 ) Q (X) L C W Q (C) L η X > η c Q (C) H W + Q (X) L W + Q (C) L W Q (X) H Q(X) H Q(C) = Q (X) H (68) = Q(C) H (69) > W Q (C) H = Q(C) L H (70) Q(X) L > 0 (71) X C 24

X η = 1 Q L Q H η c = 1 T L T H (72) Q H T H Q L T L (73) X 2 2 2 Q H T H = Q L T L (74) η = 1 T L /T H 2 1 (η = 1 T L 0 ( 2 ) 2 2 100 0 η = 1 273.15 373.15 = 0.27 27% 13 Q T Q T (75) 25

d Q (76) T 1 mol (T 1, V 1 ) (T 2, V 2 ) 1 d Q T = du T + P dv T d Q T2 T = c dt V2 v T + R T 1 V 1 = c v T dt + R dv (77) V dv V = c v log ( T2 T 1 ) + R log T Q V2 dq = c V (T 2 T 1 ) + R P dv (79) V 1 2 (P T V ) (78) dq T S 1 2 S 1 S 2 d Q U2 S 2 S 1 = T = du V2 T + P dv (80) T U 1 V 1 ( V2 V 1 ) (78) ds = 1 T dq = 1 T du + P dv (81) T du = T ds P dv (82) T 1 T 2 2 X X 2 W Q 1 Q 2 W = Q 1 + Q 2 (83) 26

W Q 1 Q 2 T 1 X T 2 Q 1 Q 2 W 1 W C1 C2 2 Q 1 Q 2 T 10: C1 C2 X (C1 C2) T ( 10 ) C1 1 Q 1 T 1 C1 Q 1 T W 1 Q 1 = W 1 + Q 1 (84) C2 Q 2 = W 2 + Q 2 (85) 1 T 1 T 2 1 X C1, C2 3 T 1 T 2 1 ( 10 ) 1 T Q 1 + Q 2 W W 1 W 2 W + W 1 + W 2 = Q 1 + Q 2 0 (86) T Q 1 T 1 Q 1 T = Q 2 T Q 2 T 2 (87) 27

Q 1 T 1 + Q 2 T 2 0 (88) T < T 1, T 2 2 N i T i Q i N i=1 Q i T i 0 (89) (89) 2 2 X N i=1 Q i T i 0 (90) 2 N i=1 Q i T i = 0 (91) X Q i = T i i d Q T i (92) (92) N i=1 Q i d Q = T i T = 0 (93) dq = 0 0 2 1, 2 2 A, B 1 A 2 B 1 A B 1 d Q T + d Q T = 0 (94) A(1 2) B(2 1) 28

A(1 2) d Q T = d Q B(2 1) T = d Q B(1 2) T (95) 2 S 0[K] 3 U S 13.1 1 mol (78) n mol n 2 2 nr log 2 2 2 NA n N A n log 2 (78) 1 n ( ) U2 nc v log 2 nc v log 2 1 U 1 29

14 1 2 A 2 1 B A B Q i + T i i A(1 2) B(2 1) 2 1 2 S 2 S 1 i A(1 2) d Q T 0 (96) Q i T i (97) d Q T A () () S S B () (98) S S B (99) S 0 (100) 30

2 2 (97) 15 15.1 d Q = T ds (101) du = T ds P dv (102) (S, V ) 2 (T, V, P ) 2 S U (S, V ) ( ) ( ) U U du = ds + dv (103) S V V (102) ( ) U T = (104) S P = ( U V T 1 V ) S S (105) S 2 S 1 Q T (106) 31

1 (U 2 U 1 ) T (S 2 S 1 ) W (107) F F = U T S (108) F = F 2 F 1 W (109) F 0 (110) F F = (U T S) = U T S S T (111) df = (T ds P dv ) T ds SdT = SdT P dv (112) F (T, V ) F (T, V ) du = ( ) ( ) F F dt + dv (113) T V V T 2 ( ) F S = T ( ) F P = V V T (114) (115) F 2 F 1 W = P (V 2 V 1 ) (116) 32

G G = F + P V = U T S + P V (117) G = G 2 G 1 0 (118) G dg = df + P dv + V dp = ( SdT P dv ) + P dv + V dp = SdT + V dp (119) G (T, P ) ( ) G S = T P ( ) G P = P T (120) (121) (108) (117) F G U S(T V P ) F G U F G 1 H = U + P V (122) 15.2 1 atm 100 1 atm 99.974 373.12 K 1 atm 373.12 K G l (T, P ) 33

250 1.4 P [10 5 m/s 2 ] 200 150 100 50 P [10 5 m/s 2 ] 1.2 1 0.8 0.6 0.4 0.2 0 300 400 500 600 700 800 T [K] 0 280 300 320 340 360 380 T [K] 11: G g (T, P ) 2 373.12K P = 1.013 10 5 [N/m 2 ] G l (T, P ) > G g (T, P ) (T > 373.12) (123) G l (T, P ) < G g (T, P ) (T < 373.12) (124) T = 373.12 [K] G l (T, P ) = G g (T, P ) (125) 1atm 100 P T (125) (125) T P T P ( ) 11 T = 647 [K], P = 221 10 5 [N/m 2 ] 34

T [K] V [m 3 ] () () () P [N/m 2 ]=[Pa] U [J] W [J] Q [J] S [J/K] C V, C P [J/K] c v, c p [J/K g] c v, c p [J/K mol] 1 2 3 1 mol () 4 11.1 km 20.0 km 216.65 K 11.1 km 223.46 N/m 2 5 1 mol 6 T 1 1 mol T 2 1. 2. 7 1. 2. 35

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