LV
1, 2m
LA kA
2
4, 8cm
kV o
100C
L = 2L k
P cond cond =
V
kV
+
LA 2LV kA + LA kV = kA kA kV
P cond (T H − T C cond H − C )kA kV = A 2LV kA + LA kV
kA( kA(T H H − T C C ) L
=
(51, (51, 1o C )(0, )(0, 026W/m.K 026W/m.K )(1, )(1, 0W/m.K ) 3 − 2(3, 2(3, 0 × 10 m)(0, )(0, 026W/m.K 026W/m.K ) + (0, (0, 075m 075m)(1, )(1, 0W/m.K ) = 17, 17, 68W/m 68W/m 2
k 401W/m.K 401W/m.K 4, 8 × 10
−4
m
100o C
2
L
1, 2m 16J/s 16J/s LF = 333J/g 333 J/g
53, 5o X 340K
170o X
−
dm P dt = L
cond cond
=
F
16J/s 16J/s = 0, 0 , 04804g/s 04804g/s 333J/g 333J/g
[x − (−170)] (k − 273) = [−53, 53, 5 − (−170)] (373 − 273)
3, 0mm 20
−
o
+72
o
−
F
F 7, 5cm o
X (x + 170) (k − 273) = (116, (116, 5) (100) 100x 100x + 17000 = 116, 116 , 5k − 31804, 31804, 5
P cond cond =
kA( kA(T H H − T C C ) L
x =
k = 1, 0W/m.K o
92 F 5 9
k = 340K 340K
116, 116, 5k − 31804, 31804, 5 − 17000 100 x = −91, 91, 945o X
(92o F ) F ) = 51, 51, 1o C
51, 51, 1K
o o
P cond cond = (1, (1, 0W/m.K ) A
51, 51, 1o C 3, 0 × 10−3 m
4
= 1, 7 × 10 W/m
C
2
o
T c T f f − 32 = 5 9
C
o
F
F
T T o F =
P cond T o C → T o C = 5.T o F 5
dh k(T H − T C ) = dt LF ρh
1cal = 4, 186J e 1cm = 100 m. k = 1, 674W/mK, e LF = 333 × 10 J/kg. 3
1
5T T − 32 = → 45.T = 5.T − 160 5 9 T = −4
dh = 0, 40cm/h dt
−4o F
5, 0o C
−
4, 0o C
1 , 4m 0, 12cal/m.o C.s
0, 40
20%
80% 20o C
200L 40o C 700W/m2
T C = ˘5, 0o C
T H = 4, 0o C T X = 0, 0o C L = 1, 4m kagua .A(T H − T X ) kagua .A(T X − T C ) = L − Lgel Lgelo
P =
(0, 12)A(4, 0o − 0, 0o ) (0, 40)A(0, 0o + 5, 0o ) = = 1, 4 − Lgelo Lgelo
1 cm∆T . 20 t
1 (4, 18J/g o C )(200 × 103 cm3 )(1g/cm3 )(40o C − 20o C ) . 20 (1, 0h)(3600s/h) P = 2, 3.104W
Lgelo = 1, 1m. A = 33m2 5, 0cm 20, 0g
10o C
−
0, 000o C 100o C
D = 2, 54000cm d = 2, 54508cm
cm/h 0, 0040cal/s.cm.C o 0, 92g/cm3
h
A
P cond =
k (0, 0o C )
kA(T H − T C ) h T H (−10o C ) Q = L F
T C m dQ dt
LF P cond = L F
dm dt
m = ρAh dm dt
= ρA. dh dt
= P cond
0, 000o C
Da0
ρ Da = D a0 (1 + αc T f )
T f
αc T i = 100, 0o C P n = P a − P r = 1, 05 × 103 W
De0
P n
De = D e0 [1 + αa (T f − T i )]
αa
Da0 (1 + αc T f ) = D e0 [1 + αa (T f − T i )]
T = 15o C
T f =
Da0 − De0 + De0 αa T i = De0 αa − Da0 αc
(2, 54000cm) − (2, 54508cm) + (2, 54508cm)(23 × 10−6 o C −1 )(100, 0o C ) (2, 54508cm)(23 × 10−6 o C −1 ) − (2, 54000cm)(17 × 10−6 o C −1 )
T amb = 32o C r = 2, 2cm h = 10cm ε=1 dm/dt g/s
T f = 50, 38o C
0o C LV
dm 4 = P rad = σεA(T env − T 4 ) dt
Q = c c ma T f
cc
ma
A = πr 2 +2πrh = π(0, 022m)2 +2π(0, 022m)(0, 10m) = 1, 53×10−2 m2
|Q| = c a me (T i − T f ) T env = 32o C = 305K T = 15o C = 288K e ε = 1 ca
me
dm σεA 4 = (T − T 4 ) = dt LV env (5, 67 × 10−8 W/m2 .K 4 )(1, 0)(1, 53 × 10−2 m2 ) [(305K )4 − (288K )4 ] 2, 256 × 106 J/kg
cc ma T f = c a me (T i − T f )
= 6, 82 × 10−7 kg/s ≈ 0368mg/s
cc ma T f me = ca (T i − T f ) =
(386J/(k.g.K ))(0, 0200kg)(50, 38o C ) (900J/(k.g.K ))(100o C − 50, 38o C ) me = 8, 71 × 10−3 kg
0, 5m 77, 0o C
27, 0o C
0, 850
α = 11 × 10−6 o C −1 30m
10o C 40o C
∆L A = 4πr 2 T = (273, 15 +
r = 0.500m 27, 00)K = 300, 15K
∆L = L o .α.∆θ ∆L = 30.(11 × 10−6 ).(40 − 10) = 99 × 10−4 m
P r = σεAT 4 = (5, 67 × 10−8 W/m 2 .K 4 )(0, 850)(4π)(0, 500m)2 (300, 15K ) = 1, 23 × 103 W 1, 2 × 10−5
T env = 273, 15 + 77, 00 = 350, 15K P a = σεAT 4 8
2
4
2
o
C −1 e 2 , 6 × 10−5 o C −1
αzinco > αaco Lf
c1 m1 (T 1 − 0) = c 2 m2 (0 − T 2 ) + m.Lf
78, 0o C 114o C 109kJ/kg
−
879kJ/kg 2, 43kJ/kg.K 0, 510kg 78, 0o C
m =
c1 m1 (T 1 − 0) − c2 m2 (0 − T 2 ) Lf
114o C
−
m = 53g
m 0o C
Q1 Q1 = L V .m = 879.0, 510 = 448, 29kJ
53g 0o C
100g
53g
50g 78o C
−114o C
Q2
Q2 = c.m.(T f − T i ) = 2, 43.0, 510.192 = 237, 59kJ
|Q| = c 1 m1 (T 1 − T f )
Q3 |Q| = c 1 m2 (0 − T 2 ) + m2 Lf + c1 m2 (T f − 0)
Q3 = L f .m = 109.0, 510 = 55, 59kJ
0o C T f
Q = Q 1 + Q2 + Q3 = 742kJ
c1 m1 (T 1 − T f ) = c 1 m2 (0 − T 2 ) + m2 Lf + c1 m2 (T f − 0) 50g
200g
25o C
T f = 2, 5o C 15o C
−
45o F
1a 0o C 2a
C F − 32 = 5 9
0o C 3a 0o C
0o C
∆C ∆F = 5 9
T f = 0o C
|Q| = c 1 m1 (T 1 − 0)
C 45 = 5 9 C = 25
150g o
20, 0
220g 300g
C
5, 0g 100o C
P 3 = 80mmHg
Qagua = c agua .magua .∆T + Lvapor .msolido o
= (1cal/ C )(220g)(100o C − 20o C ) + (539cal/g)(5, 00g) = 20, 3kcal
P 3
80mmHg N 2
373, 35K P N = ( 273T ,16 )P 3 =
Qtacho = c tacho .mtacho.∆T = (0, 0923cal/g o C )(150g)(100o C − 20o C ) = 1, 11kcal
,35 ( 373 )80 = 109, 343mmHg 273,16
T i
0, 0056mmHg
Qagua + Q tacho = ccilindro .mcilindro (T i − T f ) 32o C
L0 3, 77m 25 × 106 /o C
Qagua + Qtacho + T f ccilindro .mcilindro 20, 3kcal + 1, 11kcal = + 100o C = 873 o C o (0, 0923cal/g C )(300g) T i =
x
127, 08g 63, 54g/mol
24, 5J/kmol
Q = c.n(T f − T i ),
c = 24, 5 × 10−3
e n =
127, 08 =2 63, 54
Q = 24, 5 × 10−3 .2(2T i − T i ) = 49 × 10−3 T i J
l0 = L0 /2 l = l 0 + αl0 ∆T lo
x
100K
l
900K
196kJ 24, 5J/kmol
2
2
2 0
2 0
2
x = l − l = l (1 + α∆T ) − l
2 0
(1 + α∆T )2 = 1 + 2α∆T + (α∆T )2
Q = c.n(T f − T i ),
Q = 196 × 103 ,
n = x2 = l 02 (2α∆T ) → x = l 0
(2α∆T )
x = 7, 5 × 10−2 m
c = 24, 5 × 10−3 e ∆T = 800
196 × 103 24, 5 × 10−3 .800 n = 1 × 104
