0 (Preliminary) F G T S pv (1)

Transcription

1 0 (Preliminary) F G S p (1) p, S (2) II (two variables function) (total differential) ( ) (1) U (2) Legendre p S F (3) (4) i c 2018 etsuya Kanagawa

2 Maxwell ( 0.4.7) Maxwell [ A] [ B] Maxwell [ ] Joule [ A] Joule [ B] [p.73 (18/10/26)] [ C ( )] Mayer Mayer Joule homson [ ] Joule homson [ ] J Joule homson (material) (molecule) (component) (phase) ,, ii c 2018 etsuya Kanagawa

3 4.1.5 (phase change) Avogadro Gibbs Duhem G ( ) µ G H, F, U Maxwell µdn G [ ] ds [ ] df dg iii c 2018 etsuya Kanagawa

4 iv c 2018 etsuya Kanagawa

5 2018 II : 3F305, kanagawa kz.tsukuba.ac.jp 1. : : 10 5 ( ) [10 14 ( ) 23:59 ]: : ( ) [1]: : ( ) [2]: 4 4 : ( ) [3]: 4 5 : ( ) 5 [4]: 5 6 : 11 9 ( ) [5]: 5 7 : ( ) [6]: 5 8 : ( ) [7]: 5 9 : 12 7 ( ) [8]: 5 10 : ( ) [9]: : ( ) : 60 7, (10:10 ) 8.,. 4 1, ( ) 11:30, manaba., manaba. 3 (manaba ) I. ( ). 4,, [1] ( ). 6, ,. 8 [ ],, ( ). 1 c 2018 etsuya Kanagawa

6 II ( ) manaba, , 2018 I., I,, 12., I,. 3..,,,. I,, , ,., 9,,.,,,.,,,,.,, ( )., ( ),. 10,, ( ).,,,. 11 [ ],,,,,, (, ) I (,, ),,. [ ], HP ( ): 13 I,,, II.,. 14 [ ] 75, ( I ),,, ,,.,,. 16 [ ],,,., ( ).,,., I,,.,,. 2 c 2018 etsuya Kanagawa

7 ,,,,., manaba, , 18. : ( 0), ( 1), Maxwell ( 2), ( Joule, Mayer, Joule homson )( 3) 19. ( 4), ( 5), ( 6) , ( ), , (, manaba, ). ( ),,.,,. 18 [ ],.,,. 1,.,, 2 ( ). 19 5,.,. II.,,.. 20,,.,, (Legendre transform). 21 [ ],.,., (mechanics). (mass point) ( I). ( ) (particle mechanics),. ( ), (rigid body). (deformation), (continuum) ( ).,,,., Newton [, (Newton ), ]. (mechanical engineering) [ ( ) ], 2, 2,,.,. 3 c 2018 etsuya Kanagawa

8 0 (Preliminary) 0.1 F G II 22, F, G F U S (0.1) G H S (0.2) , U H S, F G, S p I, H H U + p (0.3) 22 [ ] (state variable), (state quantity),. ( 1). [ ].. 23 [ ] (free energy), Helmholtz ( )., (free enthalpy), Gibbs ( ). [ ] (Gibbs ), Gibbs G, (Helmholtz ), H F ( ). 24 [ ], ( 4),,, (definition),. (formula) (theorem),., (0.1)(0.2).,,. 27 G. F (0.1) 1 U, H. 4 c 2018 etsuya Kanagawa

9 G (0.2), G H S = U + p S = } U {{ S } +p = F + p (0.4) F, F G. (0.4), (0.1)(0.2)., S. 28. (0.4) G = F + p, F, G, H (0.1)(0.2)(0.3). U p 29, U S, H F 30., F G,. (0.1)(0.2),, (0.4) [ ],., 100. (, )... G = H S S, G = F + p p. 29 [ ] p, pd.,., H = U +pd U (0.5) }{{}, U pd ( ),.,, 2,,.,,. [ ], d = 1/ ( ). 30, S p ( 1 )., I ( ), 1. 31, 1, F G. 5,, 1.,, F G (, ) c 2018 etsuya Kanagawa

10 0.1.2 (0.1) (0.3), 33. : (i) ( ), ( ) 34 35, p (ii),, U, H ( U + p ) 38, S 39., (0.1)(0.2) F G 2 40., 33 [ ] : (i) (pressure) p [Pa] (volume) [m 3 ], (mechanics). (ii) 0 (the zeroth law of thermodynamics), (temperature) [K] ( I 1). (iii) 1, (internal energy) U [J]. (iv) (enthalpy) H [J], (isobaric process) ( ). (v) 2, (entropy) S [J/K] ( 0.2 ). 34 [ ] (extensive variable),, (intensive variable).,. 35 [ ] ( ) p ( ),,, ( ).,. 36 [ ] ( ),. [ ( )] [ C], [K]. [ ( )], ( ). x, x,.,,.., 5,,.,,,. 37 [ ] 3, 4 (chemical potential)., (specific enthalpy) h = H/m [J/kg] (m ). [ ] ( I). 38 [ ] Gibbs., Gibbs ( 23). 39 [ ] (reversible process),, S 2.,. (finite value)., d Q/. [ ] dx 1 x 3, 2 ( ). 40 [ ] p, (, U, H, S, F, G) 1 d Q 6 c 2018 etsuya Kanagawa

11 , U, H, F, G, 4, 41., U, H, F, G. 42., p S [J] , ( ) = ( ) ( ) : (0.6) du = d Q d W (0.7)., P. 41 [ 1 ],.,. 4,, ( ) ( ). 42 A = B, (i) A B. (ii) A B (A B ).,.,. [ ] A B. 43, ds = d Q/., [ 1 ] (0.1) (0.4), S p ( p) (S ) (, S p )., S, (heat quantity) ds = d Q. 45 [ ] (system). (surroundings), (boundary). 46 [ ]. ( ), ( ( : infinitesimal), )... 7 c 2018 etsuya Kanagawa

12 , U, ( ) d Q ( ) d W ,, du., d d Q d W, d 49., 2 : (i) 50, 51, ( ) d p, d W = pd (0.8)., [ ] (heat quantity) (work),,., ( ), ( ) [ ].. I,,,,. 50 [ ].,. 51 [ ] (displacement), (force). 52 I, (0.8). (0.8). 8 c 2018 etsuya Kanagawa

13 (ii) 53 S ds d Q (0.13), d Q, d Q = ds (0.14) 53 [ ],, ( )., ( ), :,. 54 [ ] (irreversible process), S, ds d Q (0.9) (Q ).,.,, ( 5),. 55 [ ] : ds = d Q d. ( ), ( ).. [ ] ( ). 56 [ 49 ] ds S. (thermal equilibrium state) 1 2 (definite integral), : S 2 S 1 S = 2 1 d Q (0.10) [ 2 ] : (i) ( = 0 ), S = 2 1 d Q 0 = d Q = Q (0.11). 2 (integrand) (isothermal), 3 Q d Q., Q (ii), d Q 0, : ds = 0, S = 0, S 1 = S 2 (0.12) [ ( )],. 9 c 2018 etsuya Kanagawa

14 . (0.13), , ,. (i)(ii), (0.7) 59 60, 61 62, : du = ds pd (0.15) (0.15) 63.,,. d, d. 2., (0.8). 57 [ ], Clausius d Q/,.,,.,, , (0.14) ( 0.2.1). 59 [ ],, (0.7) (conservation law of energy)., (0.15), S,., (0.15), ( ).,,., (0.15), 3 ( ),. 60 [ 59 ] ds = d Q, (0.15).., ( ), (i),, (ii) (0.15),,, (0.15),. [ ], (0.15). 61 [ ]. ( ),. [ ],,. [ ],., 1 1,. [ (counterexample)] 2,, ( ). 62 [ ],., 4, (reversible) (quasi-static) ( ). 63,,., (0.15), I ( 4, ). 10 c 2018 etsuya Kanagawa

15 2. (0.15) ( ) F d = U d p d (0.16) 2 ( ) G d = H d + dp (0.17) 2 [ ] (0.1)(0.2), (0.18) 65, (0.15). (0.16) : ( ) ( ) F U ( ) = d = d S = Ud du ds ds pd = U d + }{{ 2 } 67 } {{ } ds = ( ) (0.21) 64 1., (0.8) (,. ). 65 ( 4), : d(fg) = f dg + g df (0.18) ( (derivative) (differential quotient)), (differential),. 66 (0.17) (0.16),, ( 1.3) dh = ds + dp (0.19).,, (1.22) 1, 1, ( 1 ), : d 1 d = 2 = d 1 = 1 d (0.20) 2 ( ), ( )., df ( ).,,. 11 c 2018 etsuya Kanagawa

16 0.2.1 (1) p, S, S [ (0.13) (0.14)] 68.,,, (0.14)., p,,, S 4 : (i). p (ii), , S 73. ds,.,, ds d. 68 (0.7) ( ), (0.8). 69 [ ].,,.,., ( ) ( ).,,, ( ).,. : (i) ( ), (ii) ( ), (iii),., ( ) ( ),. [ ],. 70,., ( ), ( ).,, (heat input),,, (heat output). 71 [ ],, 20 C ( C ). 3 : (i), (ii), (iii),. 72,,.,.,,,.,.,,,,.,,,.,.,, ( ) ( ).,. 73.,. 12 c 2018 etsuya Kanagawa

17 ,, 2 74 : d W = pd (0.8) d Q = ds (0.14), ( ) p ( ) d., ( ) ( ) ds 75., , (2),. d,, 74 [ ]. 99 % ( ),,.,,,,. 75 (0.14),,., ( ) d Q,, ( ) ds ( ). d d,, ( ). [ ] d Q ds,,, S. 76 d Q = d, S. S [J/K], 1 K. [ ] p S,, (p ), ( S). 77, S.,. d W = pd, p d Q ds. 78 [ ], ( ), ( ).. [ ],, ( )., ( ).,,, ( ).,. 13 c 2018 etsuya Kanagawa

18 79. (0.7) : d Q = du + d W (0.22) , 2 du = C d, d }{{} W = pd = mr }{{} d }{{} & (0.23) 82., (0.22) : d Q = C d + mr. d (0.24), 1 C d = C + const. (0.25) ( ) 83, 2 mr d = mr d (0.26)..,. 79 [ I].,.. (fundamental theorem of calculus). 80,. 81 [ ] d Q.,,. 82 [ ] C [J/K], m [kg], R [J/(kg K)]., c [J/(kg K)], C = mc., I. 83 [ ]. [ ] C, c, R., I m. [ ] 4,. 14 c 2018 etsuya Kanagawa

19 ,,., d Q =??? (0.27).. I 2 1 d Q Q 1 2 (0.28), 86.,. (0.26)., (0.24) ( 0), : d Q = C d + mrd (0.29) ( ) : d C + mr d = C ln + mr ln + const. (0.30),., d Q, d Q (0.31) 84, = p/(mr) = (p, ).,, p 2, (p, )/ d.. 85.,,,. 86,, Q [ ] Q ( ). 87 [ III] (variables separable). 88 [ ], ln, (base) Napier ( ) e = , 10 log,.,,. 15 c 2018 etsuya Kanagawa

20 , d. d Q/,, d., ( ).,, d Q ds (0.32), ds 89. : (i) d,. (ii) d,. (iii),,. (iv),, II, ( 3) 91.,,., ( 1),, Maxwell ( 2) 92. I,,, ,.,. [, ],. 90 [ ].,.,.,,.. 91, Boyle Charles. 92,.,. 93 d I, ( ). 16 c 2018 etsuya Kanagawa

21 0.4 I, II, III,,.,,., (two variables function) f x y, x y, f(x, y) 95., x y, f 96. f x y II , 94 [ ],.,,. [ ],,,. [ ] (differentiation), :, ( ), pp. 1 6, [ ] ( ) (independent variable), ( ) (dependent variable) ( (unknown variable) (unknown function)). 96, f, x y.,. (point). (curve).. 97 [ ] z = f(x, y)., f (x, y) z ( ), z.,. 98 [ I, II] 1 y = f(x), x, y, 1, 2,., 1 (inverse function), f, x = f 1 (y), x, y (x y ). [ ] 2,,., ( 0.4.6). 99 [ ] 1., Boyle, Charles, Poisson. 2 1,,,,. [ ],, [ ] 3 2, 4 3 ( n )., II, 1 2,, 2 3 n., 2 ( ), 1 ( ). 17 c 2018 etsuya Kanagawa

22 ., 101 : p = mr = p(, ), = mr p = (p, ), = p mr = (p, ) (0.33) p,, , 103,, (total differential) x y ( ) 105, f(x, y) 106., df(x, y), df(x, y) = df(x, y ) + df(y, x ) }{{}}{{} x y = f f dx + dy (0.34) x y 101 [ ] m [kg] (mass), R [J/(kg K)] (gas constant). 102 [ ], 2 ( 4 )., p ( ). 103 [ ], t, v(t)., x, δ(x) ( )., (t, x), u(t, x) p(t, x) (x = (x, y, z) ).,,,.,,, [ ],,,., (i) 1, 1. (ii), [ ], x y [ ] f(x, y), 3 : (i) x y, (ii) x, (iii) y.,, (i) = (ii) + (iii)., (0.34).. 18 c 2018 etsuya Kanagawa

23 (i) f/ x, y , f x lim x 0 f(x + x, y) f(x, y) x } {{ } y ( ) ( = lim x 0 ) f x (0.35) , f/ x 114, x f ( ). f/ x x dx, ( f/ x)dx, x f, 115. f/ x, ( f/ x)dx, y ( (0.34) 1 ) 116. (ii). x dx f ( f/ x)dx, y dy f 107,, (0.34) [ ] dx dy. 109 [ ] (0.34) 2,., (differentiability),. (proposition), ( II). [ ]. 110 [ ] y [ ] x f. 112 [ ], x, a., x,,.,,. [ ] aylor (higher-order terms), ( ). 113 ( ), f f(x + x, y) f(x, y). 114 [ ]., ( ), ( ), ( ),. [ ],,. 115 [ ] f/ x,., (i) f(x, y) x (verb),, (ii). 116 [ ] (0.34) 2 1, y. x y, (i) dx y, x., (ii) f/ x y (0.35). [ ] (0.34) 2, c 2018 etsuya Kanagawa

24 ( f/ y)dy, f ( ) df(x, y) : f x dx + }{{} x f f y dy }{{} y f df(x, y) }{{} f (0.36) (iii) df, dx, dy (, ) 119, ( ) (iv), (0.34)., y 122, dy = 0, df(x, y), df(x, y) y=const. = f dx (0.37) x , x y, 117 [ ] d, (infinitesimal)., 1 dy/dx, (finite value). (fractional number) ( d ). 118 [ ], 10 30, ,, 1/.,,,. 119 [ ], ( 1 ). 120 [ ( )] (product), (sum),., (0.34) 2 ( ) = + = + = = ( ) ( ).,. 121 (,, ),.,, ( ). [ ],, f/ x. 122 y x. 123 [ ], : df y=const. = f x dx, df y = f dx (0.38) x 124 [!!!] (0.37), d, df(x, y) y = df dx = (0.39) dx.,, dx, df., f 2 f(x, y). y 20 c 2018 etsuya Kanagawa

25 . (0.37) ( 3). 4., 125. d(fg) = f dg + g df (0.18) [ ] fg h 126, h, h(f, g)., 2 (0.34). 3., 2 z = f(x, y) y f/ y., 1 y = f(x) f(x, y, z) df(x, y, z), y(x) dy/dx, y(x) x(y) 127 dx/dy., : dy dx = 1 dx/dy (0.40),, dx dy dy dx = 1 (0.41) 128., 1 dy/dx, dx dy 129., y. [ ].. 125, I, [ ] ( : mapping) f, y = f(x) x = f 1 (y)., f. 128 [ I] (0.41) (composite function). 129 [ ] 100 % (, ).,,.,,. 21 c 2018 etsuya Kanagawa

26 , 2 f(x, y). II, f x 1 x/ f (0.42) 130., 2 131,, x y,.,.. 1, 2, 3, d dx f(x), f(x, y), x f(x, y, z) (0.43) x,, f , arcsin x, arccos x, arctan x 133. (0.40), y., (chain rule). [ ] x = r cos θ = x(r, θ) y = r sin θ = y(r, θ), ,, 2, 2 ( ) , f(x, y). x2 [ ] x 2 (exponent) 2, x 2, ( x) 2. (1 ). : 2 ( ) 2 f x 2 = 2 x 2 f = 2 ( x) 2 f = f (0.44) x , (sine), (cosine), (tangent) : d dx arcsin x = 1 1 x 2, d dx arccos x = 1, 1 x 2 d dx arctan x = x 2 [ ] (inverse trigonometric function), sin 1 x. 1/ sin x = (sin x) 1., 22 c 2018 etsuya Kanagawa

27 0.4.4, C P, ( I): dh = C P d, C P = dh d (0.45) H 1 135, dh, (0.19), C P = dh d = ds + dp d (0.46). 3. I, ( ),, 2, 1 ( 3.2 ).,, C P = H(, p) (0.47)., H (0.3)., (i) dh H 137, (ii) / x,. 135, H 2 ( 4 3 )., H 1,. [Joule ( 3.2 )] 1, U = f( ), H U + p = U( ) + mr = H( ) ( ) dh, H. 137 [ ] ( ): C P = H(, p), : C P = H(, p) S + p ds + dp = U (U + p ) = + p ds + dp d 23 c 2018 etsuya Kanagawa

28 (2 ) 138. (p,,, S, U, H, F, G, ) 2.,,. 2,, 139, 140., (Boyle Charles ) p = mr = (κ 1)U (0.48) 141., 1 p = mr/, 2 p = f(, ) (0.49), 2 p = (κ 1)U/, 2 p = g(, U) (0.50) 142.,, (0.49) (0.50) U., 2, (0.49)(0.50) 143. (0.49)(0.50), f g.,, , 3 n. 139 [ ] Boyle ( ) Charles ( ),, 2 ( ), , ( ( ) ). ( ).,. 141 p = (κ 1)U., Boyle Charles ( 3.2, ). [ ] κ c P /c, c P c. 142, ( ). 143, f g.. 24 c 2018 etsuya Kanagawa

29 . p. f g, p(, ) p(, U) } {{}} {{} U (0.51)., p/, p/, ( ) , p,., (0.51) ( ), 1.,.,, p(, ) ( ) p (0.52), ,, ,. 145 [ ], (,, ) ( ),,., (i), z = f(x, y),, ( ). (ii), p(x, t), p t x. (i)(ii),,.,. 146 [ ] , ( A), ( B). ( ). 148,, : p(, ) ( ) p(, ),,, 1,. ( ). ( 1).. 25 c 2018 etsuya Kanagawa

30 , : ( ) ( ) x y = 1 (0.53) y z x z ( ) ( ) ( ) x y z = 1 (0.54) y z z x x y ( ) ( ) ( ) ( ) y y y t = + (0.55) x z x t t x x z ( ) ( ) ( ) y y t = (0.56) z t z x (x, y, z, t), (p,,, S). x (0.53). 2 z, 1 (0.41) 2, ( ). (0.54). 3 (x, y, z) 2, 1., 3. ( (x, y, z) ) (0.53), (0.54) 1. (0.53)(0.54), (x, y, z). x, y z., 2., 2, 3. : x f(x, y, z) = 0 (0.57). (0.57),, (x, y, z), 149 [ ], ( ), pp ( ). 150 (denominator), (numerator), (subscript), (x, y, z) 1 (circulation),. 1 ( ) (0.41) c 2018 etsuya Kanagawa

31 (0.53) (0.56) 152.,,. (0.55)(0.56), 3, (0.53) (0.54) , ( 1) (0.53), x = x(y, z) y = y(z, x) 159.,. dx(y, z) dy(z, x), ( ) x dx(y, z) = y ( ) y dy(z, x) = z z ( ) x dy + z ( ) y x dz + x y z dz (0.58) dx (0.59) 152, 2. 4 (0.53) (0.56),,. 153 (0.56) (0.55)(0.56) 4 (x, y, z, t),, 4 3. (0.53)(0.54), 2,. [ ] 1, 1, ,., ( ).,,., (0.55)(0.56). 156 (0.54), II (Jacobian Jacobi ) ,,,. 158, 2 3 : f(x, y, z) = 0.., [ ] (i), x, (y, z). (ii) x, 1, 2. (iii) (0.54), z = z(x, y),. 27 c 2018 etsuya Kanagawa

32 . (0.58) 1 dy (0.59), 160 : 1 dx + 0 dz = ( ) x y z ( ) y dx + x z [ ( x ) y z ( ) y + z x ( ) ] x dz z y (0.60) dx dz 161,, dx, (0.53) : ( ) x y z ( ) y = 1 (0.53) x z, dz, : ( ) x y z ( ) y + z x ( ) x = 0 (0.61) z y 1, (0.54)., (0.61) ( z/ x) y : ( ) x y z ( ) y z x ( ) z + x y ( ) ( ) x z z y x y }{{} (0.53) 1,, (0.53) ( ) x z y = 0 (0.62) ( ) z = 1 (0.53) x y,, (0.54) : ( ) x y z ( ) y z x ( ) z = 1 (0.54) x y 160, (0.59) (0.58). (0.58)(0.59). 161 dx dz (identity) : Adx + Bdz = Cdx + Ddz A = C B = D 28 c 2018 etsuya Kanagawa

33 ( 2) (0.53), 2 z., (0.58), dz = dx = ( ) x dy (0.63) y z, dx ( 0) 165, : ( ) x dy y z dx = ( ) x y y ( ) y = 1 (0.64) x z 1, d 166. (0.59), y (z, x) 2., (z, x) ( z) 167, ( )., (0.54). (0.58), dx = 0 168, dz 169 : ( ) x dy y z dz + ( ) x = z y ( ) x y z ( ) y + z x ( ) x = 0 (0.65) z y, (0.53) 162 ( 1),.,. 163 : (0.53), x = x(y, z) y = y(x, z),, z, 1, dx dy, 1 (0.40), 1. dy dx 164, z. 165 dx = 0. dx = 0 ( x ), x, x, (0.53) ( ). 166,.,, 2. ( 1) ( 2). 167 z, z. 168 x. (0.58), z y, x. 169 [ ] d,,.. 170,, y (x, z) 2 29 c 2018 etsuya Kanagawa

34 , ( 1) P (x, y) Q(x, y) : P (x, y)dx + Q(x, y)dy (0.66),. z(x, y) dz(x, y) = P (x, y)dx + Q(x, y)dy (0.67) ( ) z dx + x y ( ) z dy = P (x, y)dx + Q(x, y)dy (0.68) y x., dx dy, : P (x, y) = ( ) z, Q(x, y) = x y ( ) z y x (0.69) 2, (0.69) , III, 174 : ( ) P = y x 6. (0.70). ( ) Q x y (0.70),, dx = 0 x, x., y 2, 1, ( ). 171 [ ] 2 ( ). 172 (0.67) ( ) (0.66). 173 [ ] (necessary condition), (sufficient condition), (necessary and sufficient condition).,. 174 [ ] (0.69) (0.70).. 30 c 2018 etsuya Kanagawa

35 7. (0.67) (0.68) 175,, dz(x, y) = ( ) z dx + x y ( ) z dy = P (x, y)dx + Q(x, y)dy = 0 (0.71) y x z(x, y) = C (0.72) 175 (,, ). 31 c 2018 etsuya Kanagawa

36 (C ) [ ] 1., , [ 176 ] n n ( ).,. ( ),.,, ( ) (. 3 ). 178 [ ] 177 ( ),. (i), ( ) 1 df dx = 0 (0.73) ( ).,, 1.,,,. (0.73), x, (C ): f(x) = C (0.74) (ii), 2 ( ) 1 f(x, y) x = 0 (0.75).,. x ( ), C y ( )., (0.75) f(x, y) = C(y) (0.76).,, ( )., C y,. 179 [ ], (0.75) C(y) C(x) C.,. ( ), x, (0.75) ( ).,., [ ] f(x, y) = C ( C ).., (0.75), ( ), (0.75). [ ],.,, ( III). 32 c 2018 etsuya Kanagawa

37 1 U, H, F, G, (0.1)(0.2)(0.3), F, G, H,, Legendre ( ),.,.,, ( ) , 185,,, 186.,,.,,.,.,., 2 187, [ 0] 4, ,.,. 183,. 184.,, 3.,. 185, (10 9 ), (10 6 ). 187 [ ] 2,, ρ = m/, v = 1/ρ = /m (m ) [ ],.,. 189 [ ],. 33 c 2018 etsuya Kanagawa

38 2,, 190. ( ). ( 20 C).,,, ,.,, ( ) (1), (0.15) 195 : du = }{{} ds p }{{} d (1.1) (1.1), ( ) ds d. U 2 S, [ ] ( ),.,,,. 192,,. ( ).,,.,,. 193 [ ],.,,, ( ). 194 [ ],., Maxwell ( 2)., ( ),,,. [ ], ( ). 195 [ 1],.. [ 2], d Q = ds,, ( 0). 196 [ 4 ( )] 3, c 2018 etsuya Kanagawa

39 197. (1.1), du(s, ) = ds pd (1.2) }{{}., du(s, ) : du(s, ) = ( ) ( ) U U ds + d (1.3) S S (1.2) (1.3) du(s, ),, : ds pd = ( ) ( ) U U ds + d (1.4) S S (1.4), ds d ( )., ds d, : ( ) U = = (S, ) (1.5) S ( ) U p = = p(s, ) (1.6) 2 p, U , U U(S, ) S 197 [!!!] U(S, ). ( ), [ ( 0.4.2)],. 199 [ ( )] 2, 1., ( ),, (subscript). 200 [ ] 2 ( ), U,, S. 201 [ ],.,,.., ( ),,. (1.5)(1.6).,,, ( I )., ( ).,. 35 c 2018 etsuya Kanagawa

40 ,, U(S, ) 202. S, U 203.,, (S, ), U. (1.1) (1.2) (thermodynamical identity), (1.2) U(S, ), 204., (1.2) : du(s, ) = (S, )ds p(s, )d (1.7) U U(S, ), U(p, ) 205.,. (i) ( 1.0.1),, U(p, ) 206. (ii) du(p, ). (iii), (1.1) 207, 208., U(p, ). U(S, ) (S, ) [ ( )]., (S, ) ( ). 203 [ ],.,. 204 [ ] (thermodynamical potential), (thermodynamical characteristic function). 205 [ ] U(S, ) U(p, ), U., ,,. 207 [ ] (1.2). (1.1) (1.2). 208 A dp + B d = C ds + D d.,,. 209,,.. 36 c 2018 etsuya Kanagawa

41 , U, p ( (1.5)(1.6)).. 2, 2 ( ), (1.5)(1.6),,, 214.,., ( ) ( ).,, ( ) ( 1.0.1).,,,. 210 [ ],.., F Ω, F = Ω/ x (x ). [ ] ( ), ( ). [ ] ( ) v Φ (v = gradφ).,,.,..,. [ ],,,. 211 [ ] ( ),..,,,,. 2,,.,.,.,.,, ,, ( )., [ ],,, ( ) (,, )..,,, ( 1 ), ( ).,. 214 ( ),,.,,. 37 c 2018 etsuya Kanagawa

42 1.2 (2) ( (1.1)),, (4, 215 ) , Legendre p S 218 Legendre ( ) 219,, ( ). p., U(S, ), (S, ).,, S.,, 1. S 220. U(S, ),., (1.5), 221., F (, ) 222, ( 215, Maxwell ( 2), Joule, Mayer, Joule homson ( 3). 216, II [ ], 2., 3, II,. 218, (, 2014). 219,, ( ). [ ] (analytical mechanics) Legendre. 220, , p., p. 222, (0.1).,. 38 c 2018 etsuya Kanagawa

43 1) U(S, ) (1.5) 223 : (S, ) = ( ) U S U S 0 U F } S {{ 0 } F (1.8) F. U : ( ) U U = S + F = (1.9) S }{{} S + F }{{} (1.9) 2, F (0.1),, F U S (0.1). F 224, U S. (1.9) 1 ((1.8) ), F S., S 223.,,. [ ] U, S,,, (1.8)(1.9), F (linear function)., (1.9) : ( ) U U = S y = ax + b = dy dx x + b (1.10) S + = ( ) U S + F (1.11) S (slope) a (= dy/dx), ( ), = ( U/ S). (intercept) b, F. 226,. : = ( ), 1., (S, ), U(S, )..,. 227 [ ] (i) ( ), (ii) (U ), (iii) 39 c 2018 etsuya Kanagawa

44 p ( ( ) ( ) ), ( ), 1., Legendre. 8. (0.1) (0.4), Legendre F, F (, )..,. F (0.1) ( 229 ) : df = d(u S) = du d( S) = } du {{ ds } Sd (1.13) (1.1) 1 2, (1.1), 230. df = Sd pd (1.14), 2 F (, )., ds Sd (S ): U S U S U S 0 U F S 0 (1.12) 228 Legendre., p S. 229 [ ].,.,., ( ),,., df, df(t, x).,, du. [ ], du, du(, ),. 230 [ ]. (1.13), (1.14).. ( )..,,,,,. 231 [ ( 1.3)] pd dp. 232 [ ( 0)]. 40 c 2018 etsuya Kanagawa

45 (1.14), (1.1),, 233. (1.14), F ( p S ), (, ) 234., F (, )., F (, ) df (, ) = ( ) ( ) F F d + d (1.15) (1.14) 235, U, ( ) F S(, ) = ( ) F p(, ) = (1.16) (1.17)., F = F (, ) 236., ( ).,,,. : i) ( 1/ ) ( 1) (1/ ). ii) (2/ ). iii) (1 + 1/ 1). (1.14), : i) S, d, Sd ii) p, d, pd iii) Sd pd., df [ ] (1.14),,,., (1.14), F (1.1). ( ).,. 234 [ ] (1.14), F ( p S ) (, ).,, 2., (1.14), (i) (, ), (ii) ((1.15) ), (iii) (1.16)(1.17).,. 235 (1.14), df, df (, ). 236 F (, ), (1.14) (1.15). 41 c 2018 etsuya Kanagawa

46 F (, ),, 237., S, F (, ) (1.16).,, ( )..,., (0.1) (1.16)(1.17). Legendre, F,, (1.13) (1.14). (1.13).. (i), 3 239, df = du ds Sd (1.13). F F (U, S, ), 3 df (U, S, ), du, ds, d.,, 2, (ii) (1.13). F = U S, d d., ( ).,. 237 [ ] F (, ),., F (, p) F (S, ) (.. ) Legendre.. (0.1)(0.2)(0.3),., ( ),, ( ),. 239 [ 4 ] 3.,, , 2,.,. 241 [, ] F 3,. 42 c 2018 etsuya Kanagawa

47 242. ( ), (1.15),. F, H, G, 4,,. 1.3 (3) 3, 4, 243., 2. 2 F (, ), 1 U(S, ), 3 U(S, ) 244. F (, ),., p ( ),., ( ) 245.,.,, , 1 = ( ) F U,S (1.18) 1. [ ] (C ): 242 [ ]. F (, S, U) = U + C(, S) (1.19) 243 [ ], 2,., ( ).,.,,,.,. 244, , ( ). F,, (0.1) , 2,. ( ). 43 c 2018 etsuya Kanagawa

48 ( 1) U(S, ) p(s, ) (1.6) 247 ( ) ( U U H p(s, ) = S H (F ), ) (1.20) H = U + p (0.3). (1.20) H., (0.3), H 248.,., H, 3. H (0.3), 2 (1.1) 249, : dh = }{{} du + pd }{{} (1.1) + dp = }{{} ds + dp (1.21), 3, 2., dh = ds + dp (1.22) 3., I,,, 250. (1.22), H (S, p) 247 [ ] U, S,, p 4. (1.6). [ ] H. H. 248 U + p. 249 (1.22) (1.1)..,. 250,,. (1.22) ( ). 44 c 2018 etsuya Kanagawa

49 , dh(s, p)., H(S, p) dh(s, p) = ( ) H ds + S p ( ) H dp (1.23) p S. (1.22) dh = dh(s, p)., (1.22) (1.23) 251.,, H(S, p) : ( ) H (S, p) = S ( ) H (S, p) = p p S (1.24) (1.25), H, I , H(S, p)., (0.3),, (4) 3 U(S, ), F (, ), H(S, p),., H(S, p), ( ) S. 251, 2, ds dp. 252 [ ( I)], ( ), ( )..,,..,,,.,,.,. 253 [ 252 ], ( ).,.,,. 254, H(S, p),.,, H. 45 c 2018 etsuya Kanagawa

50 255., S. p H.,.,., ( 3) H(S, p) (S, p) (1.24) : = ( ) H H G S p S G,, (0.2) : (1.26) G = H S (0.2) G (, p). (0.2) G 256 : dg }{{} = } dh {{ ds } Sd }{{} = dp Sd (1.27) (1.22), 4, : dg = Sd + dp (1.28) (1.28), G , (1.28), G = G(, p) 259., G(, p) dg(, p) = ( ) G d + p ( ) G dp (1.29) p 255 [ ] H(S, p) G(, p). [ ] H, S, p, [ ] 1 1 2, 3 ( ) (1.22), (1.28),,. 258 [ ],,,..,,. (, ). 259 [ ], (1.28) dg = dg(, p). 46 c 2018 etsuya Kanagawa

51 ,,, S : ( ) G S(, p) = ( ) G (, p) = p p (1.30) (1.31),, p G(, p)., 4 G(, p) Legendre, F, H, G ( ) 4 4, 4. : (i) U, F U S, H U + p, G H S 4 262, 260 G F G(, p) F (, ).,, ( 5 ). 261 [ ],.,., ( ). : (i),, (ii) [ ],., F (p, S).,, F,.,,. 47 c 2018 etsuya Kanagawa

52 4 263 : du = ds pd (1.1) df = Sd pd (1.14) dh = ds + dp (1.22) dg = Sd + dp (1.28), (ii) U, F, H, G, ( ) 265., (1.1)(1.14)(1.22)(1.28) 2. U, F, H, G : U(S, ), F (, ), H(S, p), G(, p) (1.32) (1.32). (0.1) (0.3). (1.1)(1.14)(1.22)(1.28), (0.1) (0.3),, 266. (iii) (1.32), (1.32), (1.1)(1.14)(1.22)(1.28), (1.5)(1.6)(1.16)(1.17)(1.24)(1.25)(1.30)(1.31)., 1 2 (2 263 [ (. )], ds pd,. (i). [J]. (ii). ( ),. 264 [ ], (1.32),,,. [ ],,. [ ], [ ] ( : ), ( : ).,. 266, (1.32). 48 c 2018 etsuya Kanagawa

53 ). : ( ) ( ) U(S, ) H(S, p) = = S S p ( ) ( ) U(S, ) F (, ) p = = S ( ) ( ) H(S, p) G(, p) = = p S p ( ) ( ) F (, ) G(, p) S = = p (1.33) (1.34) (1.35) (1.36), (1.33), 1 (S, ), 2 (S, p) 267. (iv) 2,., (1.33) (1.36), p,, S , 4 2, ( ),, (S, ), (, ), (S, p), (, p),, U(S, ), F (, ), H(S, p), G(, p) ,,. (v) (1.33), ( ) 2 S, ( ) 267 [ ].,., ,, ( ),., p, S, ( 0) , (combination), 4C 2 = 6, 4 ( ). 2 ( ) , (. ) (1.32). 49 c 2018 etsuya Kanagawa

54 (vi) (1.33) (1.36),. ( )., S,., (1.36) ( 1), ( 2) 274., 1 2., 275. (vii), F, H, G 277,, 4 (1.1)(1.14)(1.22)(1.28) (1.33) (1.36),...,. 273 [ ], 1, 1, ( ) ( ).,.,, ( ).,,,., 80, 10.,,,. 274 [ (combustion)] (Otto ( ) ) (1.36) 1, (Diesel ) (1.36) 2,.,, 1., 2. ( (3 ) (3 )). 275, ( II),. 276 ( Boyle Charles )..,. 277 [ ] U, F, H, G 4, 2 : (i), (ii) [J]. 278 U,. 279 [ ] I, ( ) ( ). 50 c 2018 etsuya Kanagawa

55 7., 4 U(S, ), F (, ), H(S, p), G(, p) (1.33) (1.36) , U, F, H, G 282.,, : (i). (ii) (Legendre ), (i) ( ). (iii), (ii). (iv) (i) G(, p).,,.,..,, (1.33) (1.36), 1 ( ) 2 ( 2 )., (1.33), ( ) ( ) U(S, ) H(S, p) (S, ) =, (S, p) = S S p }{{}}{{} (S, ) (S, p) (1.37). [ ], II ( ) ( ). 280 (1.5)(1.6)(1.16)(1.17)(1.24)(1.25)(1.30)(1.31). 281 ( 6),.,, U(S, ), F (, ), H(S, p), G(, p) ( 264 ). 282,. Legendre. F, H, G,.. 51 c 2018 etsuya Kanagawa

56 283.,.,, (p, ) 284.,, (1.33) ( ).,,, 285.,, ( 3 ) (1.33) (1.36), ( ).,, (1.33) (1.35), H(S, p).,, H(, ) H(, p) S p 2, H(S, p),. U, F, H, G, 288., 283 ( ). 2, p. 284, = p/(mr) = (p, ) ( 0.4.1). 285., [( ) ],. 1 ( ),, t.,. [ ( ) ] t x = (x 1, x 2, x 3 ) 2 ( 4 )., (kinematics),, (thermodynamics) ( )., (mechanics) (kinematics).,,., (statics) (dynamics) ( ), c 2018 etsuya Kanagawa

57 .,, U, F, H, G, 289.,,., ( ), ( ).,, , (1.32) G(, p), p,, G 290.,, ( ) 291., ( ),..,,, p = f(, ) (1.38) 292., 293, g(p,, ) = 0 (1.39). f g, 289,,,.,,,. 290 G. 291 [ ]., Boyle, p = C/, (C ). 292 [ I ], (1.38),. U S. 293 (1.39), 3 ( ), 3, 2. (1.39), (implicit function representation). g = 0 p f.,,, f (explicit function). f g, 3. [ ]. 53 c 2018 etsuya Kanagawa

58 ., f g , f g, 296.,, 297,., I,,.,,..., Maxwell ( 2) 8. Gibbs Helmholtz 298. ( ) [ ( )] F F U = F = 2 [= U(, )] (1.42) ( ) [ ( )] G G H = G = 2 [= H(, p)] (1.43) p p F (, ) G(, p),, 294, p = p(, ), p = f(, ) ( p f )..,,. 295 [ I] (ideal gas), f p = f(, ) mr/ (1.40) (m [kg], R [J/(kg K)]).,,,, mr. [ ( )] mr, Hooke Young, Newton ( ), Fourier ( ). 296,,,.,.,. ( ) (real gas), van del Walls ( ). 297, ( ). 298 ( ) : x 2 ( y ) ( ) y = x y (1.41) x x z x z 54 c 2018 etsuya Kanagawa

59 U(, ) H(, p) [ ] ( ) F (, ) G(, p), ( ) U(, ) H(, p). 300 [ ( )], U(S, ) H(S, p) 2, S ( )., S U(S, ) H(S, p) ( )., F (, ) G(, p) p,, ( ), F (, ) G(, p). [ ], F (, ) G(, p), U(, ) H(, p)., U H,.,. [ ] (1.5), (S, )., U(, ) = U( (S, ), ) = U(S, ). U(S, ), [ ( )],, c,.,,, ( 6 ). F G. 55 c 2018 etsuya Kanagawa

60 2 Maxwell (Maxwell s relation),. 2.1 ( 0.4.7) 302 (i) 303 dy dx = P (x) Q(y) (2.1) 304. dx P (x)dx + Q(y)dy = 0 (2.2) 305,. (ii), ( ), dy dx = P (x, y) Q(x, y) (2.3), P (x, y)dx + Q(x, y)dy = 0 (2.4) }{{}}{{} x y 306., (2.4),.,., (2.4). 302 [ ] ( 10, ), (, ( 5 ), ( 7 ), ( 10 )).,. Amazon. [ ]. 303 [ ( )] (, ),, dx., dy/dx. 304 [,, ] y(x) ( ), x, P (x) Q(y) x y ( ). 305, (2.1) dx,.,, ( ). 306 (2.2) (2.4), (variables separable) (exact), ( ),., 1. [ ] (2.1) (2.3),, (x) (x, y). 56 c 2018 etsuya Kanagawa

61 P (x, y)dx + Q(x, y)dy (0.66). (0.66), z(x, y) dz(x, y)., : P (x, y)dx + Q(x, y)dy = ( ) z dx + x y ( ) z dy = dz(x, y) (0.67) y x, , (0.67), 310 : P y = Q x (0.70) [ ]. (0.67) : P (x, y) = z x, z Q(x, y) = y (0.69) P y, 311, : P y = y ( ) z = x x ( ) z = Q y x (2.6) 307 [ ] (0.66). ( 232). 308 [ ], P Q (x, y), P dx + Qdy.,.,. 309, [ ] dx dy (differential)., (0.66) ( ). ( ),. 311 [ II] 2 z(x, y). (i), 2 z x y 2 z. (ii) 2 y x. (i) (ii),, 2 : 2 z x y = 2 z y x (2.5),,. 57 c 2018 etsuya Kanagawa

62 2.2 Maxwell ,, U(S, ), F (, ), H(S, p), G(, p) 4 ( ) : d U(S, ) = (S, ) ds p(s, ) d (2.7) }{{}}{{}}{{} df (, ) = S(, )d p(, )d (2.8) dh(s, p) = (S, p)ds + (S, p)dp (2.9) dg(, p) = S(, p)d + (, p)dp (2.10) (2.7) (2.10),, U(S, ), F (, ), H(S, p), G(, p) 317,,., (2.7) (2.10), U(S, ), F (, ), H(S, p), G(, p) 318.,,.,. 312 [ ] Maxwell,,,. 313 [ ] I,,, 1, ( ).,. 314, [ ] U, F, H, G,., 1. [ ],,.,. 316 [ ], du du(s, ).,. 317 [ ] (2.7) (2.10),. ( 1.5.3). 318,.,,. 58 c 2018 etsuya Kanagawa

63 , (2.7) ds, du(s, ), = ( ) U S ( ) U = (S, ), p = = p(s, ) }{{} }{{} S (2.11) , [ A] 2.2.1, (2.7) (2.10), (0.70) 322., (2.7), du(s, ) = }{{} (S, )ds p(s, )d = }{{} ( ) ( ) U U ds + d (2.12) S S. 2 (0.70), : ( ) ( ) p = S S, Maxwell 1. (2.13), 3 (2.8) (2.10) (0.70), 3 Maxwell. : 319 [ ],.,.,,. [ ] f(x, y) = xy + y 2 y, x + 2y., x. 320 [ ]. [ ], S, (S, ) 2 (S, ). 322,,.,.,.,. 59 c 2018 etsuya Kanagawa

64 Maxwell (1 ) ( ) ( ) p = S S ( ) ( ) p S = ( ) ( ) = p S S p ( ) ( ) S = p p (2.13) (2.14) (2.15) (2.16), ( ) d, ( ) ( / ) p.,, [ ] ( ), ( ) ( )., ( ). (i),,., ( ) ( ( ), ( ) ). (ii) d, ( 1/ ),. (iii), ( ). ( ) v = dx/dt,. [ 1] 3, ( ),. [ 2],, (line integral) ( II, ). 324 [ ] [ II ( )] Maxwell. Jacobian (Jacobi, ), (2.13) (2.16) ( ): J (, S) (p, ) / p S/ p / S/ = 1 (2.17) 325 [ 324 1] Jacobian., (determinant), (row) (column) ( ): J (, S) (p, ) / p / S/ p S/ = / p S/ p / S/ (2.18) 326 [ 324 2] J, (variable transform) : d ds = J dpd (2.19) 60 c 2018 etsuya Kanagawa

65 (2.14) (2.16), (2.13) (2.15) ( 3 ). (2.13) (2.16)., 3, : (i) ( ), [J] ( p [J] S [J]) (ii) 1 (p,,, S) (iii) 10. (2.13) (2.16), (i)(ii)(iii) [ B] 327 [ A],, 328., (2.12), 2 ds d., ds d., (1.5)(1.6) : ( ) U = S ( ) U p = S (1.5) (1.6), (1.5), S, ( ) S = }{{} (1.5) [( ) ] U = S S S [( ) U ] } {{ S } (!!) = }{{} (1.6) ( ) p S (2.20)., 329, (1.6), Maxwell 1 (2.13) [ III] (0.70) ( 2.1 ). [ ], ( ) [ B]. 329, U, S,. 330 ( ) [ B], ( ).,, [ A]. 61 c 2018 etsuya Kanagawa

66 2.3 Maxwell.,,, (1.33) (1.36), 4 ( ) U, F, H, G 331, 4 p,,, S., (2.13) (2.16), ( p, ), F G,,., 333. (2.13) (2.16) ( ), p,,, S 4, 334, 4.,, ( ), ( ) (closed set/system)., , [ B],. [ A] [ B],,,. 331 [ ], U, F, H, G.,. 332 [ ]. ( ), ( ). 333 p p, S S,., F U,,., ( ). 334 [ ] (2.13), p, S., (2.14), p S,., (2.13) (2.16), p,,, S 4,.,. 335 [ ] 1 : x + y + z = 0, x + y z = [ ],, ( ).,. (computational mechanics). 337 [ ],, Newton 62 c 2018 etsuya Kanagawa

67 (2.13) (2.16) (2.13) (2.16).. (i) (2.13) (2.15), S., S Navier Stokes (2 ) (exact/analytical solution),., 100., (numerical/computational study), (approximate solution)., (perturbation method), (weakly nonlinear phenomena). [ ],. 338 [ ], Cauchy Riemann ( ), 2., ( ). 339 [ ], ODE (ordinaty differential equation), PDE (partial differential equation). 340 [ ]., ( ), ( ).,,. ( III), 1,.,,., ( 2 ) ( ).,,., ( ) ( 337). 341 [ ( )] 2 (quadratic curve) ( : analogy), (diffusion equation), (wave equation), Laplace,, (parabolic), (hyperbolic), (elliptic).,. 63 c 2018 etsuya Kanagawa

68 ,, 345.,,,. (ii) (2.14) (2.16), p,.,, S 346.,, p, S., (2.14) S(, ) = ( ) p d + S 0 (2.21) (S 0 ) 347. (2.21) p = f(, ), [ ( )],. (i), S, d Q = ds ( ). (ii) (i), S ds = 0, d Q = 0 ( > 0 ).,.. (iii),, d Q < ds. (iv) (iii), ds = 0 d Q < 0. d Q = 0.,,,. (v) (ii), > 0 (, ). 343 [ 342 ], S, (2.13) (2.15).., 2.,.,. [ ],,,.,. 344 [ 343 ] 1,, d Q = ds.,,,. 345 (2.15) (2.14) [ ], ( : arbitrary constant) C. [ ] S 0 ( ) c 2018 etsuya Kanagawa

69 , (2.14) (2.16), (2.13) (2.15)., F G.,, (0.1) (0.2). 3,, Maxwell (2.14)(2.16),., Maxwell.,,. 2,. Maxwell, (2.21),. S = mr ln + C (2.27), C. [ ] Boyle Charles,, p = f(, ), S = g(p, ) (, g ). ( 3.2 ). 349 [ ( )].,,,., Maxwell, β ((2.14) ) α ( (2.16) ). [ ],,.,,.,,. 5 : (speed of sound), (isothermal compressibility), (isothermal bulk modulus), (coefficient of thermal expansion), (thermal pressure coefficient): ( ) p : a (2.22) ρ S ( ) : (2.23) κ 1 : k : α 1 ( ) p ( ) p : β p ( p ) = 1 κ (2.24) (2.25) (2.26) 65 c 2018 etsuya Kanagawa

70 10. Maxwell (2.13) (2.16) ( ) ( ) [ U p ( p ) ] = p = 2 ( ) ( ) [ ( )] H = + = 2 p p p (2.28) (2.29) 12. Maxwell (2.13) (2.16) [ ],,,.,., S. 3.2,,. Boyle Charles. 351 [ 1]. [ 2] 3 ( 0.2) ( 3 ). [ 3]. [ 4].,. 352,.., (2.13) (2.16),.., c 2018 etsuya Kanagawa

71 3,, Mayer, Joule homson ,.,,. (1.1),, S 356.,, Maxwell (2.14) (2.16) 357,.,, , ( II), ( ) [ ] (, ). 355 [ ], 3 (general relation), (, (, 1995)).,,.,. 356 [ ],,. S. 357, U(S, ), F (, ), H(S, p), G(, p) p,,, S (1.33) (1.36). 358 ( I)., Joule (Joule ) Mayer,. [ 1] I, Mayer. [ 2] Joule homson,, (real gas) ( 3.3). 359 ( 3.1), Mayer ( 3.2), Joule homson ( 3.3),, 3.,, Maxwell,,.,. 360 [ I, II, III ],,,,.,,,,,,,.,,. [ ] ( ).,.. 67 c 2018 etsuya Kanagawa

72 [ ], 1.5.4,.,, (i) Boyle Charles ( ) p = mr = f( ) }{{} (3.1),, (ii) [ ] (3.1), 362. pv = R (3.2) p = Rρ (3.3), v ( /m = 1/ρ) [m 3 /kg], ρ ( m/ = 1/v) [kg/m 3 ], m, R [ ] 364 ( ). p = f(, ) (1.38) g(p,, ) = 0 (1.39) [ ] (1.38) 2., 2, p, 2 f 365. (1.39), [ ( )] (i).,,. 362,, (Boyle Charles ). 363 [ 1] R 0 [J/(mol K)] M [g/mol],, R = R 0 /M [J/(kg K)] ( k = 10 3 ). [ 2] R 0, R. 364 I [ ] ( ), ( ). 68 c 2018 etsuya Kanagawa

73 ( ) 366., f g, [ ], ( )., 2, 3 ( ). [ ] (1.39) (implicit function).,,.. 367,.,. 69 c 2018 etsuya Kanagawa

74 3.1 Joule, Joule ( ). 368.,,, [ A],. F p (1.17) ( ) F p = (1.17) F,, ( ) F p = ( ) U = ( ) (U S) = ( ) ( ) ( S) U + = }{{} 371., : ( ) U = + ( ) S (3.4) ( ) S p (3.5), 2 U S 1, 1., U(, ), U(S, ) 368. (measurement apparatus), (error)., ( ). 369 [ ] p ( ) p [J], F (1.17).,. ( ) ( S) 371 2,,. 70 c 2018 etsuya Kanagawa

75 372. (3.5), (1.1). (3.5) d, (1.1) ,. (1.17),, (3.5), 1 S.., S, Maxwell 4 (2.13) (2.16)., (2.14) 377, : ( ) U ( ) p = p }{{} (3.7) 372 [ ],, U.. U (S, )., U,. 373 [!!], (3.5) d..,,.,. 374 [ 373 ( )] df/dx f/ x, d/dx / x., 1,, df/dx df dx,, ( ). df/dx dx, df ( ). 375 [ ( 1.2)] (1.17), F ( )., ( ).,,,. (1.17),,. 376 [ ] 375., (1.17),..,,, ( ) ( ). 377 [ ].,. Maxwell,, ( ) ( ) S p = (3.6).,,.,,., (i), (ii), = +. (ii),. 71 c 2018 etsuya Kanagawa

76 Joule, (3.7).,. (3.1), (3.7) 1 : ( ) p ( ) (mr/ ) = = mr ( ) = mr 1 = p (3.7),, : ( ) U(, ) (3.8) = 0 (3.9) , U = f( ) }{{} (3.10)., f( ) ( 1 ).,, f( ) 378 (2.14)......,,. 379 [ ],.,. 380 [ ( )] ( ) 1. [ ] ( ( ))., 2,, (elliptic), (parabolic), (hyperbolic) c 2018 etsuya Kanagawa

77 (3.10) Joule 385, 386., 381 [ ( )] (3.10),,, (3.9)..,,,,. [ ] (3.9) (3.10),, [ 381 ] n, n., n, n ( ),.,,, ( ),,. [ ].,. 383 [ ( )] du/d = 0, U = C (C )., (,,., ).,, ( C). [ ]. 2,.,.,,., U, f( ), f( ) = C (C ) [ III ( )] (i) (general solution), (particular solution), (singular solution),. (family of curves). (ii),. (iii),. (iv). (v) ( ). 385, ( ),. Joule,,. 386., ( I, ). 73 c 2018 etsuya Kanagawa

78 Joule, (3.10) ,, Joule.,, Maxwell 391,, , (3.7) , (3.7) 1 ( p ),, 387 [ ][Joule ( ) ] A B (valve), A ( ), B (vacuum)., ( ) (rigid insulation)., A B. 388 [ 387 ( )],,, A + B,., ( )., ( A B ),,,,.,,. 389 [ 387 ( )],., Joule,., U(, ), : U(, A ) = U(, A + B ) = U = f( ) (3.11) ( ), ( )., Joule (3.9) ( ) U = 0 (3.9). (3.11). (3.11) (3.9). [ ], (, 1989), pp [ 387 ( )] Joule 2., (1843 ) ( I). 391 Maxwell.. (3.5).,,. 392 [ ]. (3.5). [ ],,,,,. 393 ( ( )) ( ). 74 c 2018 etsuya Kanagawa

79 p = f(, ) f,., ( )., (3.7), U., (3.7) p,, 394., U [ B] [p.73 (18/10/26)],,, 395. (1.1) : du = ds pd (1.1), (1.1) U S, U(, ) S(, ) d ( 0) 398 : ( ) U =, 399. ( ) S p (3.5) 394,, Maxwell (2.14). 395,,., (3.7),,,.,,,. 396 ( ) [ A], du(, ) du(s, )!! 397 ( ) [ ],, (S, ), (, ). [ 1]. [ 2] (, ).,,,,. 398 [ II],,.,. [ ], d = 0,. d. (18 ). 399 [ ] (3.5),, d du d = ds d p (3.12) 75 c 2018 etsuya Kanagawa

80 , (, ). 1, d, Maxwell (2.14). 2, (2.14) , Maxwell (2.14)., 3.1.1, (3.7). (1.1),, (3.5),. (3.7) (,, ) , 405,.., 1 ( ) 2 ( ),. 400 [ ( )], 1 ( ),. p, (1.1) ( H) (, )., (3.5). [ ( )], U(, ξ),,, ξ. 401 [ 400 ] du = ds pd,. U, (S, ), (, )., U ( ),,.,. 3, [ ] U = f(, U).. ( ) [ ] (1.1),, ( ) (3.7). [ ] Maxwell (2.13) (2.16) , I,,,.,,,. [ ],, ( ).. 405, (1.1) (3.5), (, )., 2 ( 0.4.5).,,. 76 c 2018 etsuya Kanagawa

81 3.1.5 [ C ( )] 406 [ B] (3.7) ( (3.5)),, d 407.,,. 1.1, U U(S, ), p 408. (1.3), S,, U 3., U(S, ) S, 1, S = S(, ξ) 409. S, 1 S U 406,., (, ): Kanagawa,. and aira, H., Educational Efficacy of Derivation Method for Partial Differential Equations in hermodynamics, American Journal of Educational Research, ol. 5 (2017), pp ( ), ( 0.4.2), 3.1.4,., U, / ( 0.4.3)., [ B],,. 408 [ ]. (0.15) ds d,., U = U(S, ), du(s, ) : ) ) du(s, ) = ( U S ds + ( U S d (1.3), (1.1) du = du(s, ), (1.3) (1.1)., ds d, : ( ) ( ) U U =, p = (1.5) S S 409 [ ] U(S, ) 2, S S = S(, ξ),. = (S, ξ), (3.5)(3.7).,, ( ) ( ) U = p (3.13) S ξ S ξ. ( S/ ) ξ, (0.53), (3.5) ( )., S,. 77 c 2018 etsuya Kanagawa

82 , 2 ξ S(, ξ), ds(, ξ) = ( ) S d + ξ. (1.3) ds : [ ( U ) du(s(, ξ), ) = S + ( ) ( ) ] U S d + S ξ,, ( ) ( ) S dξ (3.14) ξ ( ) U S ( ) S dξ ξ (3.15) du(s, ) = du(s(, ξ), ) = du(, ξ) (3.16) }{{} ξ. (3.16), (3.15), du(s, ) du(, ξ)., du(, ξ) du(, ξ) = ( ) U d + ξ ( ) U dξ (3.17) ξ (3.15), d dξ, ( ) U ( ) U ξ ξ ( ) ( ) U U = + S S ( ) ( ) U S = S ξ ( ) S ξ (3.18) (3.19) 2.,, 3 4 (0.55)(0.56),. 410, S 2, ξ = ξ = p.,. 411 [ ] ξ (, : xi), x. 78 c 2018 etsuya Kanagawa

83 (1.5) (1.6) (3.18), ( ) ( ) U S = p + ξ ξ (3.20)., ξ =, (3.5)., (i) (3.5) (3.7). (ii), (3.7), Joule (3.9) (3.10) = f( )p (3.21), f( ) 1 ( ). (i) Joule (3.10). (ii) (3.21), (3.21).. [ (i)] (3.7) 1, (3.21), ( ).,, Joule (3.10). [ (ii)] f( ) =., f( ),, f , (0.55)( (3.18)), U,, S, (quadratic function), (polynomial),,. 79 c 2018 etsuya Kanagawa

84 15. ( ), (1.22), : ( ) H p = ( ) ( ) S + = + (3.22) p p ( ) 1, Maxwell S 416,. [ A], (1.31). 16., H. (i) (3.22). [ ], (3.22) 1,., : ( ) H p = 0 (3.23) p, H = g( ) 417., g( ) 1,. (ii) (3.22) 418. [ ] (0.3), Joule (3.10) (3.1) : H U + p = f( ) + mr = g( ) (3.24) }{{} 414,, (3.5)(3.7)..,. 415 [ ] H(S, p) (2.9)., (2.9) (1.22).. ( )., H(, p). 416 [ ] (2.14) (2.16) 2., H(, p)., H, H(S, p). [ B], dp. S. 417, H = g( ), H = H( ). 418 (3.22), Joule (3.10),,. 80 c 2018 etsuya Kanagawa

85 Mayer.,,, C c C/m 421.,,. 2 C, C = C(, ) (3.25), 1. 1, 2 : (i) C P p 2, (ii) C 2 ( ): C P = C P (, p), C = C (, ) (3.26)., C, d Q d d Q = C (, ) d (3.27) }{{}!! 419 [ ],, ( I).,,.,,. 420,,.,,. 421 I [ ],.,, C., ( )., d Q, d, C. 423 [ ( )] (3.27), : C = d Q d (3.28),, ( ), ,, 81 c 2018 etsuya Kanagawa

86 I ( 4.3),, C P C, ( ) ( (Mayer s relation)) ,. 425, Mayer : C P C = ( ) ( ) p p (3.29) C P C, ( 1) 2 C : d Q = C(, )d (3.27) ( 2) 427 : d Q = du + pd (3.30) S.,. (3.27), d /d., d Q d., 1. [ ], d, 1., 2. [ ],,,..,,. 424 [ ], Mayer, ( ) ( ),,, Mayer.,,. 425.,,. 426,,,.,. 427,, ( ). 82 c 2018 etsuya Kanagawa

87 d Q, d Q = ds (3.30), 428. ( 3) U, (, ) : (i) (3.27) d,. (ii) (3.30) 2 d, , d, 432., : du(, ) = ( ) ( ) U U d + d (3.32). d d, (3.27)(3.30), ( )., (3.27)(3.30)(3.32), 433, ,, d Q = Cd = ds = Cd = ds (3.31).,. 429 [ ]., d, d, du 3. 2., [ ] (i),, (ii). 431 [ ] (3.30) 1 U., U, U. 432 [ ] d d, U(, ).,, U(, ),. 433 [ ( )],.,. : d 0 = U(, ) U( ) }{{} (3.33),, ( ). 434 I. 83 c 2018 etsuya Kanagawa

88 ( 1), (3.27), C C : d Q = C d (3.34) ( 2) (3.30), 2 d 435 : d Q = du(, ) (3.35), (3.32) U(, ). (d = 0), U I ( 4), U ( ) ( 437). 437 [ ] ( f/ x) y, y, x., y x. y,., ( 3 ), ( 0.4.2): ( ) f x y f(x + x, y) f(x, y) lim x 0 } x {{} y, (0.35) 84 c 2018 etsuya Kanagawa

89 ( 3) U (3.32) : du(, ) = ( ) U d (3.36) (3.34) (3.36), : C = ( ) U = C (, ) (3.37) (3.26), C (, ). (3.37) 444., 438 [ ( )], d = 0, 2 : ( ) U du(, ) = du(, ) + du(, ),, du(, ) = d 439 [ ( 0.4.2)]. ( II, ),., [ ] U = U( ) 1., d : du = du d d /, U(, )/., U, U, U ( 0.4.2). [ ] ( 0.4.2),, ( U/ ),,,. 441 [ ] d Q..,,. 442, ( ),.,,., (3.37),. 443 (3.37), : U = C, du = C d,, ( 0.4.3). 444 (3.37),.,. (3.37)., 85 c 2018 etsuya Kanagawa

90 , Mayer (3.29). [ ] (3.1), 2 : ( ) p = mr, ( ) = mr p p (3.29), I : (3.38) C P C = mr (3.41) 18. C P. ( ) H C P (, p) = p (3.42) [ ]. ( 2), ( ) d Q = dh dp (3.43). 445,,. 446 mr ( ). (3.29),., (p,, ), ( ),., (3.1), p = f(, ),. 447 [ ] I, c P = C P /m c = C /m, (3.29).,, ( ) ( ) p v c P c = (3.39) (v, ). pv = R, Mayer :, (3.29) (3.41) m. v p c P c = R (3.40) 86 c 2018 etsuya Kanagawa

91 ,, ( 3) H(, p) 448 dh(, p) = ( ) H d + p ( ) H dp (3.44) p 449.,, (3.44) , C : C P C ( ) = du d, C P ( ) = dh d (3.45) (i) (3.37)(3.42),, (3.45), C P C 1.. (ii) (3.45), 452. U( ) = C ( )d + U 0, H( ) = C P ( )d + H 0 (3.47) [ ] (, p). (3.43) 2, d dp.,. 449 p., [ ] I,,.,,,., (3.45), 1.,, [ ],, (1 ).,. [ ] U 1., (3.45),., (iii) (3.50).., I. [ ], (3.45), U = U( ), 1., C( ),. 452 [ ],, 0 C (θ)dθ (3.46)., θ (dummy variable)., 2, 0 1,. 87 c 2018 etsuya Kanagawa

92 , U 0 H 0, U( 0 ) = U 0, H( 0 ) = H (iii) C C P ( ), U H (1 ) : U( ) = C + U 0, H( ) = C P H 0 (3.50) [ (i)] Joule (3.10), U = U( ) (3.37), 2 1, 457., (0.3), Joule, H U + p = U( ) + mr = H( ) (3.51) }{{},,. 453, 0 = 0 K,,., U( 0 ) = U 0 = 0. (3.51), = 0 = 0 K, H( 0 ) H( 0 ) = U( 0 ) + mr 0 = 0 + mr 0 = 0 (3.48), U( 0 ). 454 [ ], (3 )., U 0 = H 0 = [ ], c c P,,, : u = c + u 0, h = c P + h 0 (3.49) 456 [ ], U = f( ) U( ),., U f,. 457 [Joule ], Joule (3.10), Joule ( 3.1), ( 3.2).,. 88 c 2018 etsuya Kanagawa

93 [ (ii)] (3.45) d, [ 0, ] 458 ( ) = 0 du d d = }{{} = U( ) U 0 = 0 du = U( ) U( 0 ) 0 C ( )d = ( ) (3.52), (3.47). H( ). [ (iii)] C ( ): U( ) = C 0 =0 d + U 0 = C + U 0 (3.53) 20., S 459, F, G,.. S = C ln + mr ln + S 0 (3.54) F = C + U 0 (C ln + mr ln + S 0 ) (3.55) G = C P + H 0 (C ln + mr ln + S 0 ) (3.56), S 0, U 0, H (3.1), U H 462. p = κ 1 H = (κ 1)U (3.57) κ 458 [ ], 0,. 459 [ I ],. 460 [ ],, ( ), S, F, G ( ). [ ] (3.54) (, p) (p, ) [(3.54) ], (1.1), (3.1).,., I.,,. 462 ( ).,,,,,. (3.1) (3.57). 89 c 2018 etsuya Kanagawa

94 , κ c P /c = (c + R)/c = 1 + R/c [ ] (3.50) U 0 = H 0 = 0, (3.1) Mayer 466, Mayer (3.29). C (, ) C P (, p) (3.37)(3.42), (i) (0.56) 467, (ii) 463 [ ] 2,,,., : (i), p, = p mr = (p, ). (ii) U H, (3.57) (3.50). (iii) S, (3.54). (iv) F G, (3.55)(3.56)., p, U, H, S, F, G.,,,,. 464,,. ( I 4.4). [ ( )] (ratio of specific heats), heat s. (2 ). 465, U H, κ R, : U = C = mr κ 1, H = C P = mκr κ 1 (3.58) 466 [ ],., d Q = ds., Maxwell., Maxwell ( 2.2). 467 [ ] ( 4 ), ( (3.70))., 1 dy dx = dy dt dt dx (3.59) c 2018 etsuya Kanagawa

95 H(S, p) U(S, ) 468 (S, p) (1.33) : ( ) ( ) ( ) ( ) H H S S C P = = = p S p p p ( ) ( ) ( ) ( ) U U S S C = = = S }{{} }{{} (1.33) (3.60) (3.61)., (i), (ii) S,, C P C, : [ ( S ) C P C =. p ( ) ] S (3.62) 1 S(, p), 2 S(, ), , ds(, p) ds(, ) 468 [ ] H U. ( ) H 469 [ ] (1.33),, = S p,. H, U : (i) H., H, H. (ii),, H H(, p), H(S, p). (iii), S (, ) ( ) (. ), ( ) H H S H S. (iv) =, = p S p p S p., S [J]. (iv) U(S, ), p, ( 3 ) H(S, p). 470 [ ] (. ). [ ] U(S, ) H(S, p), p. [ ], S. H(S, p) U(S, ),, S., S.,. 471 [ ], S., S(, p) S(, ). 472 (3.62), S,, ( ), : ) ) ( S p ( S (3.63) 91 c 2018 etsuya Kanagawa

96 473 : ( ) S ds(, p) ( ) S ds(, ) d + p ( ) S dp (3.64) p ( ) S d + d (3.65) (3.62) Mayer (3.29)., S,, p, 4,., d, dp, d (3.64) (3.65), d 2 475, dp d., p = p(, ), 476 : dp(, ) ( ) ( ) p p d + d (3.66) (3.66) (3.64) 2 dp, (3.64), ( ) S ds(, p) = [ ( S ) = d + p p + ( ) S p ) ( S p [( ) ( ) p p d + ) ] [( ) S d + p ( p ] d ( p ) ] d (3.67) (3.62). [ ] ( ). 473 [ ],,,,. 474 [ ]., [ ] (i) 3. (ii) 2, 1.,,,. (iii) d, 2, d. (iv) dp d., dp. (v) dp(, ), dp d d. 476 [ ] = (, p). [ ],. [ ] S, S. 92 c 2018 etsuya Kanagawa

97 (3.67) 1,, ds(, p) = ds(, p(, )) }{{} (, ) = ds(, ) = }{{} ( ) ( ) S S d + d (3.68), (, p) (, ) , (3.68). (3.67)(3.68), ds(, ).,,, d d. (i) d, 3 (0.55) 479 : ( ) S = ( ) S + p ( ) S ( ) p p (ii) d, 4 (0.56) 480 : ( ) S = ( ) S ( ) p p (3.69) (3.70). (3.62), 477 [ ] (i) S, p (S(, p)), (ii) p, (p(, ))). (iii), S, (S(, p(, )) = S(, )).,. 478 [ ], S(,, p).. 3 ( ). 479 [ ],,,. : ( ) ( ) ( ) ( ) y y y t = + (0.55) x z x t t x x z 480 ( 3.1.5), (0.55)(0.56),. [ ],, (0.55)(0.56).,, ( ),. (0.55)(0.56),. [ ] ( ). [ ], (3.69)(3.70) (0.55)(0.56).. 93 c 2018 etsuya Kanagawa

98 (3.69)., (3.62), : { ( S ) (3.62) = p [ ( S ) p + ( ) ( ) ]} S p = p ( ) S ( ) p p (3.71) S , Maxwell (2.16) , Mayer (3.29) : C P C = ( ) ( ) p p (3.29) (3.29) 2, mr,, ,, : C P > C (3.72) 481 [ (Maxwell )] ( S/ p)., ±( / ) p.,, : (i) S, (, p)., G(, p). G (1.28). (ii), ±Sd ± dp ( )., (, p),, U, F, H, G [ ]., 2, S. (2.16).,,. 483,. Maxwell ( ). 484 [ ] (2.16)., G = H S., = (, p) ( ), (2.16) (2.14)., F G. 485, mr. 486 [ ],, (thermodynamical inequality). 487, (c P > c ). 488, C..,.., C P, (3.29), C., (3.29). 94 c 2018 etsuya Kanagawa

99 , (i) C S (3.60)(3.61) 490. (ii) (3.69)(3.70),, (3.71). (iii) Maxwell, Mayer (3.29) ( ) ( ) p p C P = C (3.74) S ( ) ( ) p + C = 0 (3.75) 24. (3.30), d Q = C d + S [ ( ) ] ( ) U p p + d = C d + d (3.76) (0.55) ( ), : [ ( ) S C P C = ( ) S = ( ) ] [ ( ) S S = ( ) ( ) ( p = p p ) + p ( ) ( ) S p ( ) ] S (3.73), Maxwell (2.14)., (2.16),,. 2, 3 (0.55)., (0.55),.,,. 490 [ ], Mayer ,,.,,. C (. I ). 493,,,.,, 1 1,. 95 c 2018 etsuya Kanagawa

100 [ ] C (, ) (3.37), U(, )., : du(, ) = ( ) U d + ( ) ( ) U U d = d + C d (3.77), (3.37)., (3.30), (3.76) 1., (3.7), d [ ], (3.76). [ ] (3.76) Mayer, ( ) p ds = C d + d (3.81) ( ) ds = C P d dp (3.82) p 26., [ ],,,,, ( ). [ ], (3.76) C (, )., C P (, p), C P, = (, p)., (3.76) d, dp.,,,.,, p ( ): [ ( ) ] d (, p) p = d + p ( ) dp p p = ( ) d p (3.78) p, (3.76), 1 (3.78), [ ( ) ( ) ] p d Q p = C + d p (3.79) p., C P, d Q p = C P (, p)d p (3.80) ( )., Mayer (3.29) c 2018 etsuya Kanagawa

101 (i) C P C 496. ( ) CP p ( ) C ( ) 2 = 2 ( ) 2 p = 2 p (3.83) (3.84) (ii) : ( C ) = 0 (3.85) 497, p(, ) = f( ) + g( ) (3.86), f g, ( ). [ (i)] [ 1] (3.84) 500. (3.37), 501, (3.7) 496 [ ] ( ),.,,,. 497 [ ] (3.85). [ ],.,.,.,. [ ],,.,. 498, ( ),. 499 [ ( )] n, n (arbitrary constant)., n n ( ). 1,,, (. ). 500 (3.83). ( 1) (3.22), ( 2) Maxwell (2.16). 501 [ 311] 2, 2,,. 97 c 2018 etsuya Kanagawa

102 502, : ( ) = ( C = ) = [( ) ] U = [( ) ] U }{{}}{{} [ ( ) p (3.37) ] p = ( p ( ) ) ( ) 2 p + 2 ( ) p = ( ) (3.87) [ 2] 503 (3.61),, Maxwell (2.14), : ( ) = = [ ( ) ] S ) ] [( S = = [( ) ] S [( ) ] p = ( ) (3.88) 2,, ( ) 504. [ (ii)], p, (3.84) (3.85), 0, 2 ( ) 2 p 2 = 0 (3.89)..,, 1 : ( ) p = f( ) (3.90), 502 [ ] (3.7), F (1.14) (1.17)., F Maxwell (2.14).,, F. [ ] (3.83), (3.7), (2.16), G. 503,. 504., ( ).. 98 c 2018 etsuya Kanagawa

103 505. 1,, : p(, ) = f( )d + G( ) = f( ) d + G( ) = f( ) + g( ) (3.91), f, g, G, G g, 1 G, g , [ ], ( ),,,.,,. 506,,. 2.,,.,. 507,,, C = K( ) (K ).,. 508 [ : ( III )] (general solution) ( : particular solution).,, p =, p = C 1, p = C 2, (C 1 C 2 ) (3.92) (3.89),., (3.92) (3.89) ( ), (3.89).,,. (3.92) (3.89),., ( ),,.,,,. 1, , 2., 2 1, 2 1 = c 2018 etsuya Kanagawa

104 3.3 Joule homson [ ],,.,,,., Joule homson (Joule homson effect) 510,, Joule homson (, J ) 511 : µ ( ) p H (3.93)., 512 : ( ) = 1 p H C P [ + ( ) ] S = 1 p C P [ ( ) ] p (3.94),, Maxwell (2.16) 513, 514. J (3.94). C P = ( H/ ) p [ (3.42)] J µ = ( / p) H 3 (H,, p). 515.,,, 2 510,,,.,,, (, ),. 511 J ( ).,,., 4,, µ,. 512 [ ] (i) ( S/ p), ±( / ) p ( ); (ii) (p, ), G(p, ) ; (iii) G. 513, G (2.10). 514 [ ],,,. 515,,., 100 c 2018 etsuya Kanagawa

105 (0.54) 516 : ( ) ( ) p p H H ( ) H = 1 (3.95) p 1, 3,, J,, : ( ) p µc P H = 1 (3.96) ( H/ p), 1 (0.53) 517, µ = 1 C P ( ) H p (3.98)., (3.22) 518, J (3.94) ,, (0.40) 2 : ( ) ( ) dy dx y x 1 : = 1, 2 : = 1 (3.97) dx dy x z y z 518 [ 15 ] dh = ds + dp (1.22) dp ( ) H = p ( ) S + p (3.99) p. 2, 1 p, 2, ( ),,, =. [ ],, (,, ). 519,, (3.22),, ,,., C P µ, S. S. 101 c 2018 etsuya Kanagawa

106 3.3.2 [ ] J H (1.22) dh = ds + dp (1.22), S. S, (H,, p),, µ, H, ds(, p) : ds(, p) = ( ) S d + p (3.100) (1.22) 1 dh = ( ) [ S d + + p ( ) S dp (3.100) p ( ) ] [ S dp = C P d + + p ( ) ] S dp p (3.101) 521,, dh : 0 = { [ C P d + + ( ) ] } S dp p H (3.102), H dp, ( / p) H, (3.94) : ( ) = 1 p H C P [ + ( ) ] S p 27. Joule homson (3.94) (3.103) Joule homson J (3.94),.,,,., 521 (3.60). 522, C P J µ. 3.,. 102 c 2018 etsuya Kanagawa

107 ,. I, Joule, Joule homson, Joule homson [ ], J [, ( ) ].,,, ( ). 524 [ ],,,,., J, (,, ).,,. 103 c 2018 etsuya Kanagawa

108 p., H., ( )., 525 [Joule homson (1) ] Joule ( 387),.., (heat bath),,,,.,,, ( )., [ 525 (2) (throttling) ( )],, ( : pore valve). A, B, B. A A.,,., A B,. A, A,, B,. A B,,. 527 [ 525 (3) ]., A < B.,, A ( ), B ( )., p A > p B.,, Joule.,., (, ) [ 525 (4) ],,. : (i),, A B ; (ii) U = U B U A ; (iii),, p A A, ( ) A( ), W A = A 0 p A d = p A A (3.104) (,, ). B, W B = B 0 p B d = p B B (3.105), W = W B W A,, U = W = W A W B = p A A p B B (3.106), : H B = U B + p B B = U A + p A A = H A (3.107), W, (U A > U B ). [ ],, p A A = p B B, U A = U B, Joule. 529 [ 525 (5) ],., 104 c 2018 etsuya Kanagawa

109 . J,,., J,, ( ) 530.,, J µ 531 : 1 ( ) > 1 p (3.108) J,,. J inv, : inv = ( ) p (3.109),. Joule homson. J, , µ = , (200 K) (100 K),,,.,., 1908 Kamerling Onnes., (superfluidity) (superconductivity). [ ], pp , ,,. 531,,. 532,. J,,. 533,,,. 105 c 2018 etsuya Kanagawa

110 4 534,,.,.,,., ( ).,, 535.,,,, ,,.,, I., 537.,, (material) (molecule) ( ),. 538, , ( ), ( O 2 ). 534 I. 535, I II. 536,.,.,. 537, 1, ( ). 538,, (molecule) (atom) (quantum).,,,. 539,,.,, ( ), ( I 2.2.1),,. 106 c 2018 etsuya Kanagawa