Wyniki zadań z Termodynamiki

1. Podstawy termodynamiki

A.1 τ = 106 min.

A.2 c = 1853 J/(kg deg), Q = 5106 MJ

A.3
2 kg/s

A.4 N = 463 kW

A.5 Q_1,2 = 55,54 MJ, t₂ = 5,32 °C

A.6 τ = 23 min.

A.7 Δ
3387 kW

A.8 L_1,2 = L_{t 1,2} = 30 kJ, L_{u 1,2} = -3 kJ

A.9. L_1,2 = 50 kJ, L_{t 1,2} = 40 kJ, L_{u 1,2} = 30 kJ

A.10 S_1,2 = 29 J/(kg K)

A.11
= 4,4 W/K

A.12 Q_1,2 = 2,9 MJ, t_k = 87 °C

A.13 L_m = -10 kJ

A.14
-1,08 MW

A.15 V₂ = 0,35 m³, p₂ = 2,86 bar

A.16 p₂ = 3775 Tr, Q_1,2 = L_1,2 = -18,26 MJ, U_1,2 = 0

A.17 Q_1,2 = 23,68 kJ

A.18 L_1,2 = -114 kJ, L_{t 1,2} = -159 kJ

A.19 n = 1,15, V₂ = 0,17 m³, L_1,2 = -307 kJ, L_{t 1,2} = -353 kJ, Q_1,2 = -191 kJ

A.20

a) izobaryczna: T₂ = 202 K,V₁ = 14,49 m³,V₂ = 4,8 m³, L_1,2 = -1,16 MJ, L_{t 1,2} = 0

b) izotermiczna: p₂ = 3,6 bar, L_1,2 = L_{t 1,2} = -1,91 MJ

c) adiabatyczna: p₂ = 5,586 bar, T₂ = 940 K, L_1,2 = -2,4 MJ, L_{t 1,2} = -3,35 MJ

A.21

a)
= 190 kJ/kg,
= 202 kJ/kg

b)
= 218,1 kJ/kg

c)
= 224,4 kJ/kg

A.22
29,4 MW,
19,4 MW, η_o = 66%, N_o = 19,6 MW

A.23 p_k = 5 bar, Q_A = 150 kJ, Q_B = -150 kJ

A.24

Stany Parametry	1	2	3	4	5
p [bar]	1	44,3	71	71	2,3
T [K]	320	945	1494	1942	727
v [m^3/kg]	0,92	0,061	0,061	0,079	0,92

q₁ = 843 kJ/kg, q₂ = -292 kJ/kg, l_ob = 551 kJ/kg, η = 65%, N = 1102 kW

A.25

Stany Parametry	1	2	3	4
p [bar]	1	16	16	1,6
T [K]	360	792	1131	574
v [m^3/kg]	1,03	0,14	0,2	1,03

q₂ = -154 kJ/kg, l_ob = 186 kJ/kg, η = 54,7%, N = 52 kW

A.26
0,537 kg/s

A.27

Stany Parametry	1	2	3	4
p [bar]	1	8,5	21	2,52
T [K]	300	562	1367	757
v [m^3/kg]	1	0,22	0,22	1

Q₂ = -380 kJ, L_ob = 290 kJ, η = 43%, N = 580 kW

A.28

Stany Parametry	1	2	3	4
p [bar]	1	12,3	44,6	3,6
T [K]	280	579	2100	1017
v [m^3/kg]	0,0006	0,0001	0,0001	0,0006

N = 16,53 kW

A.29 T_k = 262,33 K, S_1,2 = 0,313 kJ/K

A.30 T_p = 1022 K

A.31 L_t = 486 kJ

A.32 U_1,2 = 86,38 kJ

A.33 T_k = 207 K, p_k = 0,21 MPa, L_1,2 = 1,5 MJ, Q_1,2 = 0 MJ, U_1,2 = -1,5 MJ

A.34 L_2,1 = -60 kJ

A.35 m = 1,02 kg

A.36 Q_1,2 = 414,72 kJ, U_1,2 = 296,22 kJ, L_1,2 = 118,5 kJ

A.37 Q_1,2 = -219,7 kJ, U_1,2 = 660,3 kJ, L_1,2 = -880 kJ, S_1,2 = -0,558 kJ/K, I_1,2=924,3 kJ

A.38 T₂ = 372,5 K, Q_1,2 = U_1,2 = 186 kJ

A.39 p_k = 0,622 MPa

A.40 m = 23,23 kg, Q_1,2 = L_1,2 = 14,756 MJ

A.41

a) T₂ = 75 K

b) p₂ = 666,6 kPa

c) T₂ = 1068 K p₂ = 1424 kPa

d) T₂ = 935 K p₂ = 1246,8 kPa

A.42 s_1,2 = 0,637 kJ/(kg K)

A.43 T₂ = 338,5 K, V₂ = 0,7097 m³, L_1,2 = 323 kJ

A.44 L_1,2 = 134,8 kJ

A.45 T₂ = 800 K, l_1,2 = -410,25 kJ/kg, q_1,2 = -51,2 kJ/kg

A.46 m = 1 kg, V₂ = 0,192 m³, L_1,2 = -94,71 kJ, T₂ = 399 K, u₁ = 214 kJ/kg,

u₂ = 286,2 kJ/kg, Q_1,2 = -23,66 kJ

A.47 S_1,2 = 1,1 kJ/K

A.48 Q_1,2 = -5392,33 kJ, S_{p 1,2} = -11,403 kJ/K, S_{z 1,2} = 14,987 kJ/K,

S_{c 1,2} = 3,584 kJ/K>0 (możliwy)

A.49 S_{p 1,2} = -0,2504 kJ/K, S_{z 1,2} = 0,0188 kJ/K, Q_1,2 = -5,64 kJ,

S_{c 1,2} = -0,2316 kJ/K<0 (niemożliwy)

A.50 T₂ = 900 K, v₃ = 2,58 m³/kg

2. Wymiana ciepła

B.1.
= 384 kW,
= 166 kW, k = 57%, T_e = 1272 K

B.2.
= 651 kW

B.3. t_p = 7,3˚C

B.4. α₁ = 62 W/(m² deg), α₂ = 79,5 W/(m² deg),
= 11,7 kW,
= 15 kW

B.5. α = 3,03 W/(m² deg)

B.6. q = 42 W/m², t_sw = 15,5˚C, t_sz = -12˚C,

q' = 192 W/m², t'_sw = -0,5˚C, t'_sz = -1,3˚C

B.7.
= 165 kW, t = 13,3˚C

B.8. t = 8˚C,
= 3,03 kW

B.9. δ_min = 34 mm

B.10.
= 2443 W, t = 71,3˚C

B.11. λ_z = 0,321 W/(m² K),
= 327 W

B.12.
= 7,65 kW, t_z = 78˚C

B.13.
= 611 W, t₂ = 2,05˚C, t₃ = 9˚C

B.14.
= 1,78 kW

B.15. λ_z = 0,379 W/(m² K),
= 41,3 kg/h, t_w = -10,45˚C, t_z = 12,15˚C

3. Przepływy płynów ściśliwych

C.1. v₁ =0,11 m³/kg, p₁ = 9,8 bar, T₁ = 384 K, a₁ = 392 m/s, w^* = 358 m/s

C.2. a) w₂ = 204 m/s,
=0,179 kg/s

b) w₂ = w^* = 335 m/s,
=0,22 kg/s

C.3. p₂ = 0,1243 bar (x=p₂/p^*= 0,0565)

C.4. a) p^* = 5,47 bar, T^* = 421 K, A_min = 2,69∙10^-4 m²

b) T₂ = 259 K, w₂ = 703 m/s, A₂ = 5,29∙10^-4 m²

C.5. p₂ = 1,52 bar, T₂ = 338 K,

A₃ = 0,0774 m², p₃ = 0,806 bar, a₃ = 336 m/s, T₃ = 231 K

C.6. d = 0,07 m

C.7. w₂ = 96 m/s

C.8. T₂ = 348 K

C.9. a) Ma = 1,44 (przepływ nadkrytyczny)

b) Ma = 0,72 (przepływ podkrytyczny)

c) Ma = 0,49 (przepływ podkrytyczny)

C.10. T₀₁ = T₀₂ = 811 K, T₂ = 632 K, p₁ = 190 kPa, A₁/A₂ = 2,66

C.11. a)
=2,02 kg/s, Ma = 1

b)
=1,97 kg/s, Ma = 0,88

C.12. a) T₀ = 907 K

b) T₀ = 920 K

C.13. a)
=0,179 kg/s

b) i c)
=0,183 kg/s

C.14. w₂ = w^* = 374 m/s, p₂ = p^* = 5,28 bar, T₂ = T^* = 337 K, ρ^* = 5,28 kg/m³

C.15. w^* = 438 m/s, w₂ = 744 m/s, A_min = 23,7∙10^-4 m², A₂ = 45,8 ∙10^-4 m²

C.16. T₂ = 347 K, p₂ = 1,66 bar, T₁ = 301 K, p₁ = 1,08 bar, A₂ = 0,2965 m²

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