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5kg; s ; p 1 =300kPa T 1 =60 o C

Ideal Gas. 5kg; s ; p 1 =300kPa T 1 =60 o C. 5kg; s ; p 2 =150kPa T 2 = ?. Ideal Gas. IDEAL GAS + ADIABATIC + REVERSIBLE Tv k-1 = T/( k-1 ) = c (11.12a) Tp (1-k)/k = c (11.12b) p v k = p/ k = c (11.12c). 5kg; s ; p 1 =300kPa T 1 =60 o C. isentropic. 5kg; s ; p 2 =150kPa

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5kg; s ; p 1 =300kPa T 1 =60 o C

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  1. Ideal Gas 5kg; s; p1=300kPa T1=60oC 5kg; s; p2=150kPa T2= ?

  2. Ideal Gas IDEAL GAS + ADIABATIC + REVERSIBLE Tvk-1 = T/(k-1) = c(11.12a) Tp(1-k)/k = c(11.12b) pvk = p/k = c(11.12c) 5kg; s; p1=300kPa T1=60oC isentropic 5kg; s; p2=150kPa T2= ?

  3. Tp(1-k)/k = c(11.12b) T1(Ko)p1(1-k)/k = T2(Ko)p2(1-k)/k T1 = 333K; p1 = 300,000 Pa T2 = 273K; p2 = 150,000 Pa ?

  4. Know: p1, T1, p2, T2 irreversible What is s2-s1? 200,000 Pa 388K s2 irreversible 100,000 Pa 273K s1

  5. Know: p1, T1, p2, T2 & irreversible What is s2-s1? Valid for any process between equilibrium states dQ + dW = dE Tds = du + vdp IDEAL GAS & cv and cp = const s2-s1 = cvln(T2/T1) + Rln(v2/v1) (11.11a) s2-s1 = cpln(T2/T1) - Rln(p2/p1) (11.11b) s2-s1 = cvln(p2/p1) + cpln(v2/v1) (11.11c)

  6. s2-s1 = cpln(T2/T1) - Rln(p2/p1) (11.11b) = 103[J/kg-K] ln(388/273) – 287[J/kg-K] ln(200,000/100,000) = 134 J/(kg-K) ?

  7. Know T1, p1= p2,T2 IDEAL GAS s2-s1 = ? T1 = 858K p1 = 4.5 MPa s1 T2 = 15C p2 = p1 s2

  8. 0 s2-s1 = cpln(T2/T1) - Rln(p2/p1) (11.11b) s2-s1 = 1000 ln([273+15]/858) s2-s1 = -1.09 kJ/(kg-K) 1 T 2 s IDEAL GAS & cv and cp = const s2-s1 = cvln(T2/T1) + Rln(v2/v1) (11.11a) s2-s1 = cpln(T2/T1) - Rln(p2/p1) (11.11b) s2-s1 = cvln(p2/p1) + cpln(v2/v1) (11.11c)

  9. What equation has q and reversibility in it?

  10. If reversible Q/m = q = Tds Tds = dh – vdp q = dh = cpdT 0 q = cp(T2-T1) q = -572kJ/kg

  11. Can consider ideal gas T1 = 1573oK; p1 = 2.0 MPa T2 = 773oK; p2 = 101 kPa u = ?; h = ?; s = ?

  12. Valid for any process between equilibrium states dQ + dW = dE Tds = du + vdp IDEAL GAS & cv and cp = const s2-s1 = cvln(T2/T1) + Rln(v2/v1) (11.11a) s2-s1 = cpln(T2/T1) - Rln(p2/p1) (11.11b) =143 J/(kg-K) s2-s1 = cvln(p2/p1) + cpln(v2/v1) (11.11c) u = cVT(11.2) h = cpT(11.3)

  13. increasing pressure

  14. Steady, adiabatic flow of air, dm/dt = 0.5 kg/sec, through a turbine. At inlet, V1 = 0, T1 = 1300C, p1 = 2.0 mPa (abs) At outlet, V2 = 200 m/s, T2 = 500C, p2 = 101 kPa Label state points on a Ts diagram:

  15. If isentropic: T2 = T1 (p2/p1)(k-1)/k = 670K (397C)  500C So not isentropic!

  16. What is power produced by turbine? Steady, adiabatic flow of air, dm/dt = 0.5 kg/sec, through a turbine. At inlet, V1 = 0, T1 = 1300C, p1 = 2.0 mPa (abs); At outlet, V2 = 200 m/s, T2 = 500C, p2 = 101 kPa 0 dW/dt + dQ/dt = (dm/dt) [(h2 + (V2)2/2 + gz2) - (h1 + (V1)2/2 + gz1)] z2 = z1 h2 – h1 = cp (T2 – T1)

  17. Can speed of car at 60 mph and 120 mph be considered incompressible? [0 - 1]/0 = ? < 5% then we consider incompressible M = ? < 0.3 the answer is yes!

  18. 0 = 1{ 1 + [(k-1)/2]M12}1/(k-1) M1 = V1/c1 c1 = (kRT1)1/2 [0 - 1]/0 = 0.3% M = 0.0782 V1 = 60 mph = 26.8 m/s; R = 287 J/(kg-K); 1 = p1/(RT1) = 1.201 kg.m3;

  19. 0 = 1{ 1 + [(k-1)/2]M12}1/(k-1) M1 = V2/c1 c1 = (kRT1)1/2 [0 - 1]/0 = 1.21% M = 0.156 V1 = 120 mph = 53.6 m/s; R = 287 J/(kg-K); 1 = p1/(RT1) = 1.201 kg.m3;

  20. Know p0, p and T and are asked to find V of aircraft.

  21. Know p0, p and T and are asked to find V of aircraft. M = V/c so V = Mc c = (kRT)1/2 po/p = (1 + [(k-1)/2] M2)k/(k-1)

  22. Know p0, p and M and are asked to find maximum temperature and pressure on aircraft.

  23. Maximum pressure and temperature will be local isentropic stagnation conditions. po/p = {1 + [(k-1)/2]M2}k/(k-1) To/T = 1 + [(k-1)/2]M2

  24. Know p0, p and T and are asked to find M and V of aircraft.

  25. pv diagrams for the internal combustion engine Diesel cycle Otto Cycle

  26. 0 0 0 0 1-2 doing work on system + work 2-3 & 3-4 system doing work - work Net W, , is negative so net Q, , is positive pv = c

  27. s2-s1 = cpln(T2/T1) - Rln(p2/p1) s2-s1 = cvln(T2/T1) + Rln(v2/v1) (TdS = Q)rev.

  28. s2-s1 = cvln(T2/T1) + Rln(v2/v1) (11.11a) ; Constant v, T = Toexp(s-so)/cv s2-s1 = cpln(T2/T1) - Rln(p2/p1) (11.11b); Constant p, T = Toexp(s-so)/cp Because cp>cvfor all gasses, slope of const p <constant v

  29. s2-s1 = cvln(T2/T1) + Rln(v2/v1); s2-s1 = cpln(T2/T1) - Rln(p2/p1) s2-s1=0 s2-s1=0

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