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1 270 C, 6000 C,

2 2 p T, Q

3 p: : p = N/ m 2 N/ m 2 Pa : pdv p S F

4 Q 1 g 1 1 g C cal = J

5 du = Q pdv U ( ) Q pdv

6 2 : z = f(x, y). z = f(x, y) (x 0, y 0 ) y y = y 0 z = f(x, y 0 ) x x = x 0 z z 0 = k(x 0, y 0 ) (x x 0 ). k k(x 0, y 0 ) = lim h 0 f(x 0 + h, y 0 ) f(x 0, y 0 ) (x 0 + h) x 0 k(x 0, y 0 ) = f x f x x x = x 0 z = f(x 0, y) y y = y 0 z z 0 = ( f y ) (y y 0)

7 z = f(x, y) (x 0, y 0 ) x 0 y 0 z z 0 = ( f x )(x x 0) + ( f y )(y y 0). dz = f f dx + x y dy a(x, y)dx + b(x, y)dy a y = b x, df = a(x, y)dx + b(x, y)dy

8 df (c,d) (a,b) df = f(c, d) f(a, b) (c,d) (c,d) = = 0 (a,b) (a,b) f

9 Q Q dq Q

10 : Q T c: 1 K Q c = Q T. c = dq dt. c V = ( Q T ) V, c p = ( Q T ) p C: M C = cm 1 kg 1 g J g 1 K 1

11 , g, cal 1 cal = 4.18 J g kg cal J 1 mol specific( ) J mol 1 K 1 1 mol 1 1

12 :, Extensive. 1 mol 1 g :, Intensive. =

13 p = nkt. p T k = J K 1. ( ) kt ( ) n V N n = N V.

14 1 N A = / mol( ) : u = kg. u : 12 C 12uN A = 12 g/ mol. µ m u µ = m/u. 1., N A µ g : g/ mol SI kg/ mol 1 1 g. H 2 2 g.

15 ρ: m n = ρ m., p = ρ k m T v:. v = 1 ρ., pv = k m T. 1 N A = mol 1 ν(ν = mol) V, n = N Aν V., pv = νrt R = N A k = 8.31 J mol 1 K 1

16 U V du = C V dt C V. U = 3N 1 2kT, (N, N ). : 1 c p c v = k 1 C P C V = R = N A k. N A k, R γ = C P = n + 2, n ( C V n 1 n = 3)

17 : du = Q pdv, ( U V ) T = 0, C p C V = νr, C. ν wiki P V = f(t ).

18 P V P V = νrt

19 du = Q pdv. dv = 0 du = Q. C V = ( Q T ) V = ( U T ) V. ( U T ) P = ( Q T ) P P ( V T ) P, C P = ( Q T ) P = ( U T ) P + P ( V T ) P V = V (T, P ) C P = ( U T ) V + ( U V ) T ( V T ) P + P ( V T ) P C P C V = ( U V ) T ( V T ) P + P ( V T ) P

20 ( U V ) T = 0 C P C V = P ( V T ) P P V = f(t ) P ( V T ) P = df dt df dt = C P C V df dt = νr T = 0 f = 0 P V = f(t ) = νrt.

21 1 mol 1 mol U, 1 mol V, C V, C p du pdv du = pdv du = C V dt. C V dt = pdv

22 pv = N A kt dt = N 1 A k (pdv + V dp) C V (pdv + V dp) = pdv N A k C p C V = kn A C V C p C V (pdv + V dp) = pdv γ = C p C V 1 (pdv + V dp) + pdv = 0 γ 1 γ dv V + dp p = 0 pv γ =

23 ( )

24 A B: B C: C D: D A: A p A isothermal T 1 B D T 2 Boyle s law adiabatic Poisson s law C V :

25 ? Q +, W + Q 1 + Q 2 + W = 0. Q 1 T 1 + Q 2 T 2 = 0..

26 ds = Q T Q, Q dq Q S S,, ds

27 27 C, 37 C 1000 J W T 1 = 300 K Q 1 = 1000 J T 2 = 310 K Q 2 Q 1 T 1 + Q 2 T 2 = 0 Q 1 + Q 2 + W = 0 W = Q 1 Q 2 = Q 1 + T 2 T 1 Q 1 = T 2 T 1 T 1 Q 1 = 10 K 300 K 103 J = 33 J.

28 M V S exteisive ( intensive( Q Q 2 Mpemba 50 C 90 C

29 1 J = k K K T = K k = J K 1 k x C = ( x) K 0.01 C, C ( )

30 T 1 T 2,,,,, Q ds = Q 1 T 1 + Q 2 T 2 = 0

31 W, Q 1 + Q 2 = W η η = η = W Q 1 = T 1 T 2 T 1.

32 : F (, ) F = λ dt dx. λ 10 km : ( ) ( )

33 : 1 1 2kT 1. (distribution) ρ(v x, v y, v z ) 2. f f f = f(v x, v y, v z ) ρ(v x, v y, v z )dv x dv y dv z 1 = ρ(v x, v y, v z )dv x dv y dv z

34 1. v x, v y, v z 2. v 2 = vx 2 + v2 y + v2 z ρ = (aπ) 1 3e v2 a., a v 2 = 1 (aπ) 3 v2 e v2 a 4πv 2 dv = 3 2 a, 1 2 mv2 = 1 2 m(v2 x + v2 y + v2 z ) = 3 2 kt a = 2kT m. : ρ = ( m 1 2πkT )3 e 2 mv2 kt

35 Maxwell : 2 x y ρ(x, y)dxdy = f(x)dx f(y)dy ρ(x, y)dxdy = g(r, θ)rdrdθ g(r, θ) θ g(r, θ) = g(r). f(x)f(y) = g( x 2 + y 2 ) y = 0 f(x)f(0) = g(x) g( x 2 + y 2 ) = f( x 2 + y 2 )f(0). log f(x) f(0) + log f(y) f(0) = log f( x 2 + y 2 ) f(0)

36 log f(x) f(0) = αx2, f(x) e αx2 2 E ρ(e)de 2 ρ(e) = ρ(e 1 ) ρ(e 2 ) E E = E 1 + E 2. ρ(e) = ae E kt 3:

37 L m N x v 1 v 2L mv. 2mv ( ) v 2mv 2L N p = mv 2 N L mv2 = 1 2 kt. p = N L 3kT

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5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h g(a + h) g(a) h g(x) a A = g (a) = f x (a, b)............................................ 5 partial differentiation (total) differentiation 5. z = f(x, y) (a, b) A = lim h f(a + h, b) f(a, b) h........................................................... ( ) f(x, y) (a, b) x A (a, b) x (a, b)

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