Complete Thermodynamics Cheat Sheet, Cheat Sheet of Thermodynamics

Download Complete Thermodynamics Cheat Sheet and more Cheat Sheet Thermodynamics in PDF only on Docsity! 73THERMODYNAMICS THERMODYNAMICS PROPERTIES OF SINGLE-COMPONENT SYSTEMS Nomenclature 1. Intensive properties are independent of mass. 2. Extensive properties are proportional to mass.           State Functions (properties) Absolute Pressure, P (lbf/in2 or Pa) Absolute Temperature, T (°R or K) Volume, V (ft3 or m3)   v V m= (ft3/lbm or m3/kg) Internal Energy, U (Btu or kJ)      u U m= (usually in Btu/lbm or kJ/kg) Enthalpy, H (Btu or KJ)  Enthalpy, h = u + Pv = H/m (usually in Btu/lbm or kJ/kg) Entropy, S (Btu/°R or kJ/K)   s = S/m [Btu/(lbm-°R) or kJ/!"#$ Gibbs Free Energy, g = h – Ts (usually in Btu/lbm or kJ/kg) Helmholz Free Energy, a = u – Ts (usually in Btu/lbm or kJ/kg) Heat Capacity at Constant Pressure, c T h p P2 2 = b l Heat Capacity at Constant Volume, c T u v v2 2 = b l Quality x (applies to liquid-vapor systems at saturation) is % % &'   ' & &* x = mg /(mg + mf), where mg = mass of vapor, and mf = mass of liquid.     can be written: v = xvg + (1 – x)vf or v = vf + xvfg, where vf /   '   % 0 % vg /   '   % % vfg /  &  4  = vg – vf Similar expressions exist for u, h, and s: u = xug + (1 – x) uf or u = uf + xufg h = xhg + (1 – x) hf or h = hf + xhfg s = xsg + (1 – x) sf or s = sf + xsfg 5  6    '      %%    '      &   For an ideal gas, Pv = RT or PV = mRT, and P1v1/T1 = P2v2/T2, where P = pressure, v /   m = mass of gas, R = gas constant, and T = absolute temperature. V = volume R is  but can be found from . ,R mol wt R where= ^ h R = the universal gas constant = 1,545 ft-lbf/(lbmol-°R) = 8,314 J/(kmol⋅K). For ideal gases, cp – cv = R Also, for ideal gases: P h v u0 0 T T2 2 2 2 = =b bl l For cold air standard, heat capacities are assumed to be constant at their room temperature values. In that case, the following are true: Δu = cvΔT; Δh = cp ΔT Δs = cp ln (T2 /T1) – R ln (P2 /P1); and Δs = cv ln (T2 /T1) + R ln (v2 /v1). For heat capacities that are temperature dependent, the value to be used in the above equations for Δh is known as the mean heat capacity cp` j and is given by c T T c dT p pT T 2 1 1 2 = - # Also, for constant entropy processes: ; , P P v v T T P P T T v v k c cwhere k k k k p v 1 2 2 1 1 2 1 2 1 1 2 2 1 1 = = = = - - d d d n n n For real gases, several equations of state are available; one such equation is the van der Waals equation with constants based on the critical point: , P v a v b RT a P R T b P RT 64 27 8 where 2 c c c c 2 2 + - = = = c ^ c f m h m p where Pc and Tc are the pressure and temperature at the critical point, respectively, and v   &     74 THERMODYNAMICS FIRST LAW OF THERMODYNAMICS The First Law of Thermodynamics is a statement of conservation of energy in a thermodynamic system. The net energy crossing the system boundary is equal to the change in energy inside the system. Heat Q is energy transferred due to temperature difference and is considered positive if it is inward or added to the system. Closed Thermodynamic System No mass crosses system boundary Q – W = ΔU + ΔKE + ΔPE where ΔKE = change in kinetic energy, and ΔPE = change in potential energy. Energy can cross the boundary only in the form of heat or work. Work can be boundary work, wb, or other work forms (electrical work, etc.) Work W w m W =b l is considered positive if it is outward or work done by the system. Reversible boundary work is given by wb = ∫P dv. Special Cases of Closed Systems Constant Pressure (  ): wb = PΔv (ideal gas) T/v = constant Constant Volume: wb = 0 (ideal gas) T/P = constant Isentropic (ideal gas): Pvk = constant w = (P2v2 – P1v1)/(1 – k) = R(T2 – T1)/(1 – k) Constant Temperature (    ): (ideal gas) Pv = constant wb = RTln (v2 / v1) = RTln (P1/P2) Polytropic (ideal gas): Pvn = constant w = (P2v2 – P1v1)/(1 – n) Open Thermodynamic System Mass crosses the system boundary D&  L  !Pv) done by mass entering the system. D&   6L  !  6* wrev = – ∫v dP + Δke + Δpe First Law applies whether or not processes are reversible. FIRST LAW (energy balance) / / / , m h V gZ m h V gZ Q W d m u dt 2 2 where i i i i e e e e in net s s 2 2 + + - + + + - = R Ro o o o _ i 8 8B B Wneto = rate of net or shaft work transfer, ms /  'L % &  &  us /       ' % Qo = rate of heat transfer (neglecting kinetic and potential energy of the system). Special Cases of Open Systems Constant Volume: wrev = – v (P2 – P1) Constant Pressure: wrev = 0 Constant Temperature: (ideal gas) Pv = constant wrev = RT ln (v2 /v1) = RT ln (P1 /P2) Isentropic (ideal gas): Pvk = constant wrev = k (P2v2 – P1v1)/(1 – k) = kR (T2 – T1)/(1 – k) w k k RT P P 1 1 / rev k k 1 1 2 1 = - - - d ^ n h> H Polytropic: Pvn = constant wrev = n (P2v2 – P1v1)/(1 – n) Steady-State Systems The system does not change state with time. This assumption is valid for steady operation of turbines, pumps, compressors, throttling valves, nozzles, and heat exchangers, including boilers and condensers. / /m h V gZ m h V gZ Q W m m 2 2 0 and where i i i e e e e in out i e 2 2 + + - + + + - = = R R R R o o o o o o ` `j j mo /L   6  i and e refer to inlet and exit states of system), g = acceleration of gravity, Z = elevation, V = velocity, and Wo = rate of work. Special Cases of Steady-Flow Energy Equation Nozzles, Diffusers:         X  elevation change, no heat transfer, and no work. Single mass stream. / /h V h V2 2i i e e 2 2 + = +   '   44/ , h h V V 2 where i es e i 2 2 - - _ i hes = enthalpy at isentropic exit state. Turbines, Pumps, Compressors: Often considered adiabatic (no heat transfer). Velocity terms usually can be ignored. D&      !  %   hi = he + w 77THERMODYNAMICS ENTROPY ds T Q s s T Q 1 12 1 1 2 rev rev = - = d d _ _ i i# Inequality of Clausius T Q T Q s s 1 0 1 2 11 2 rev # # - d d _ _ i i# # Isothermal, Reversible Process Δs = s2 – s1 = Q/T Isentropic Process Δs = 0; ds = 0 A reversible adiabatic process is isentropic. Adiabatic Process δQ = 0; Δs ≥ 0 Increase of Entropy Principle / s s s s m s m s Q T 0 0 total system surroundings total out out in in external external $ $ = + = - - D D D D R R Ro o o o_ i Temperature-Entropy (T-s) Diagram ∫= 21 sdTQrev s 1 2 AREA = HEAT T Entropy Change for Solids and Liquids ds = c (dT/T) s2 – s1 = ∫c (dT/T) = cmeanln (T2 /T1), where c equals the heat capacity of the solid or liquid. Irreversibility I = wrev – wactual EXERGY Exergy is the portion of total energy available to do work. Closed-System Exergy (Availability) (no chemical reactions) φ= (u – uo) – To (s – so) + po (v – vo) where the subscript o designates environmental conditions wreversible = φ1 – φ2 Open-System Exergy (Availability) ψ= (h – ho) – To (s – so) + V 2/2 + gz wreversible = ψ1 – ψ2 Gibbs Free Energy, ΔG Energy released or absorbed in a reaction occurring reversibly at constant pressure and temperature. Helmholtz Free Energy, ΔA Energy released or absorbed in a reaction occurring reversibly at constant volume and temperature. 78 THERMODYNAMICS COMMON THERMODYNAMIC CYCLES Carnot Cycle Reversed Carnot Otto Cycle (Gasoline Engine) η = 1 – r 1 – k r = v 1/v2 Rankine Cycle Refrigeration (Reversed Rankine Cycle) ( ) ( )3 4 2 1 3 2 h h h h h h − − − η = − p2 = p3 12 32 HP 12 41 ref hh hhCOP hh hhCOP − − =− −= p2 = p3 q = 0 q q w w q q T c 79THERMODYNAMICS STEAM TABLES Saturated Water - Temperature Table Specific Volume m 3 /kg Internal Energy kJ/kg Enthalpy kJ/kg Entropy kJ/(kg·K)Temp. o C T Sat. Press. kPa psat Sat. liquid vf Sat. vapor vg Sat. liquid uf Evap. ufg Sat. vapor ug Sat. liquid hf Evap. hfg Sat. vapor hg Sat. liquid sf Evap. sfg Sat. vapor sg 0.01 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 0.6113 0.8721 1.2276 1.7051 2.339 3.169 4.246 5.628 7.384 9.593 12.349 15.758 19.940 25.03 31.19 38.58 47.39 57.83 70.14 84.55 0.001 000 0.001 000 0.001 000 0.001 001 0.001 002 0.001 003 0.001 004 0.001 006 0.001 008 0.001 010 0.001 012 0.001 015 0.001 017 0.001 020 0.001 023 0.001 026 0.001 029 0.001 033 0.001 036 0.001 040 206.14 147.12 106.38 77.93 57.79 43.36 32.89 25.22 19.52 15.26 12.03 9.568 7.671 6.197 5.042 4.131 3.407 2.828 2.361 1.982 0.00 20.97 42.00 62.99 83.95 104.88 125.78 146.67 167.56 188.44 209.32 230.21 251.11 272.02 292.95 313.90 334.86 355.84 376.85 397.88 2375.3 2361.3 2347.2 2333.1 2319.0 2304.9 2290.8 2276.7 2262.6 2248.4 2234.2 2219.9 2205.5 2191.1 2176.6 2162.0 2147.4 2132.6 2117.7 2102.7 2375.3 2382.3 2389.2 2396.1 2402.9 2409.8 2416.6 2423.4 2430.1 2436.8 2443.5 2450.1 2456.6 2463.1 2569.6 2475.9 2482.2 2488.4 2494.5 2500.6 0.01 20.98 42.01 62.99 83.96 104.89 125.79 146.68 167.57 188.45 209.33 230.23 251.13 272.06 292.98 313.93 334.91 355.90 376.92 397.96 2501.3 2489.6 2477.7 2465.9 2454.1 2442.3 2430.5 2418.6 2406.7 2394.8 2382.7 2370.7 2358.5 2346.2 2333.8 2321.4 2308.8 2296.0 2283.2 2270.2 2501.4 2510.6 2519.8 2528.9 2538.1 2547.2 2556.3 2565.3 2574.3 2583.2 2592.1 2600.9 2609.6 2618.3 2626.8 2635.3 2643.7 2651.9 2660.1 2668.1 0.0000 0.0761 0.1510 0.2245 0.2966 0.3674 0.4369 0.5053 0.5725 0.6387 0.7038 0.7679 0.8312 0.8935 0.9549 1.0155 1.0753 1.1343 1.1925 1.2500 9.1562 8.9496 8.7498 8.5569 8.3706 8.1905 8.0164 7.8478 7.6845 7.5261 7.3725 7.2234 7.0784 6.9375 6.8004 6.6669 6.5369 6.4102 6.2866 6.1659 9.1562 9.0257 8.9008 8.7814 8.6672 8.5580 8.4533 8.3531 8.2570 8.1648 8.0763 7.9913 7.9096 7.8310 7.7553 7.6824 7.6122 7.5445 7.4791 7.4159 MPa 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 300 305 310 315 320 330 340 350 360 370 374.14 0.101 35 0.120 82 0.143 27 0.169 06 0.198 53 0.2321 0.2701 0.3130 0.3613 0.4154 0.4758 0.5431 0.6178 0.7005 0.7917 0.8920 1.0021 1.1227 1.2544 1.3978 1.5538 1.7230 1.9062 2.104 2.318 2.548 2.795 3.060 3.344 3.648 3.973 4.319 4.688 5.081 5.499 5.942 6.412 6.909 7.436 7.993 8.581 9.202 9.856 10.547 11.274 12.845 14.586 16.513 18.651 21.03 22.09 0.001 044 0.001 048 0.001 052 0.001 056 0.001 060 0.001 065 0.001 070 0.001 075 0.001 080 0.001 085 0.001 091 0.001 096 0.001 102 0.001 108 0.001 114 0.001 121 0.001 127 0.001 134 0.001 141 0.001 149 0.001 157 0.001 164 0.001 173 0.001 181 0.001 190 0.001 199 0.001 209 0.001 219 0.001 229 0.001 240 0.001 251 0.001 263 0.001 276 0.001 289 0.001 302 0.001 317 0.001 332 0.001 348 0.001 366 0.001 384 0.001 404 0.001 425 0.001 447 0.001 472 0.001 499 0.001 561 0.001 638 0.001 740 0.001 893 0.002 213 0.003 155 1.6729 1.4194 1.2102 1.0366 0.8919 0.7706 0.6685 0.5822 0.5089 0.4463 0.3928 0.3468 0.3071 0.2727 0.2428 0.2168 0.194 05 0.174 09 0.156 54 0.141 05 0.127 36 0.115 21 0.104 41 0.094 79 0.086 19 0.078 49 0.071 58 0.065 37 0.059 76 0.054 71 0.050 13 0.045 98 0.042 21 0.038 77 0.035 64 0.032 79 0.030 17 0.027 77 0.025 57 0.023 54 0.021 67 0.019 948 0.018 350 0.016 867 0.015 488 0.012 996 0.010 797 0.008 813 0.006 945 0.004 925 0.003 155 418.94 440.02 461.14 482.30 503.50 524.74 546.02 567.35 588.74 610.18 631.68 653.24 674.87 696.56 718.33 740.17 762.09 784.10 806.19 828.37 850.65 873.04 895.53 918.14 940.87 963.73 986.74 1009.89 1033.21 1056.71 1080.39 1104.28 1128.39 1152.74 1177.36 1202.25 1227.46 1253.00 1278.92 1305.2 1332.0 1359.3 1387.1 1415.5 1444.6 1505.3 1570.3 1641.9 1725.2 1844.0 2029.6 2087.6 2072.3 2057.0 2041.4 2025.8 2009.9 1993.9 1977.7 1961.3 1944.7 1927.9 1910.8 1893.5 1876.0 1858.1 1840.0 1821.6 1802.9 1783.8 1764.4 1744.7 1724.5 1703.9 1682.9 1661.5 1639.6 1617.2 1594.2 1570.8 1546.7 1522.0 1596.7 1470.6 1443.9 1416.3 1387.9 1358.7 1328.4 1297.1 1264.7 1231.0 1195.9 1159.4 1121.1 1080.9 993.7 894.3 776.6 626.3 384.5 0 2506.5 2512.4 2518.1 2523.7 2529.3 2534.6 2539.9 2545.0 2550.0 2554.9 2559.5 2564.1 2568.4 2572.5 2576.5 2580.2 2583.7 2587.0 2590.0 2592.8 2595.3 2597.5 2599.5 2601.1 2602.4 2603.3 2603.9 2604.1 2604.0 2603.4 2602.4 2600.9 2599.0 2596.6 2593.7 2590.2 2586.1 2581.4 2576.0 2569.9 2563.0 2555.2 2546.4 2536.6 2525.5 2498.9 2464.6 2418.4 2351.5 2228.5 2029.6 419.04 440.15 461.30 482.48 503.71 524.99 546.31 567.69 589.13 610.63 632.20 653.84 675.55 697.34 719.21 741.17 763.22 785.37 807.62 829.98 852.45 875.04 897.76 920.62 943.62 966.78 990.12 1013.62 1037.32 1061.23 1085.36 1109.73 1134.37 1159.28 1184.51 1210.07 1235.99 1262.31 1289.07 1316.3 1344.0 1372.4 1401.3 1431.0 1461.5 1525.3 1594.2 1670.6 1760.5 1890.5 2099.3 2257.0 2243.7 2230.2 2216.5 2202.6 2188.5 2174.2 2159.6 2144.7 2129.6 2114.3 2098.6 2082.6 2066.2 2049.5 2032.4 2015.0 1997.1 1978.8 1960.0 1940.7 1921.0 1900.7 1879.9 1858.5 1836.5 1813.8 1790.5 1766.5 1741.7 1716.2 1689.8 1662.5 1634.4 1605.2 1574.9 1543.6 1511.0 1477.1 1441.8 1404.9 1366.4 1326.0 1283.5 1238.6 1140.6 1027.9 893.4 720.3 441.6 0 2676.1 2683.8 2691.5 2699.0 2706.3 2713.5 2720.5 2727.3 2733.9 2740.3 2746.5 2752.4 2758.1 2763.5 2768.7 2773.6 2778.2 2782.4 2786.4 2790.0 2793.2 2796.0 2798.5 2800.5 2802.1 2803.3 2804.0 2804.2 2803.8 2803.0 2801.5 2799.5 2796.9 2793.6 2789.7 2785.0 2779.6 2773.3 2766.2 2758.1 2749.0 2738.7 2727.3 2714.5 2700.1 2665.9 2622.0 2563.9 2481.0 2332.1 2099.3 1.3069 1.3630 1.4185 1.4734 1.5276 1.5813 1.6344 1.6870 1.7391 1.7907 1.8418 1.8925 1.9427 1.9925 2.0419 2.0909 2.1396 2.1879 2.2359 2.2835 2.3309 2.3780 2.4248 2.4714 2.5178 2.5639 2.6099 2.6558 2.7015 2.7472 2.7927 2.8383 2.8838 2.9294 2.9751 3.0208 3.0668 3.1130 3.1594 3.2062 3.2534 3.3010 3.3493 3.3982 3.4480 3.5507 3.6594 3.7777 3.9147 4.1106 4.4298 6.0480 5.9328 5.8202 5.7100 5.6020 5.4962 5.3925 5.2907 5.1908 5.0926 4.9960 4.9010 4.8075 4.7153 4.6244 4.5347 4.4461 4.3586 4.2720 4.1863 4.1014 4.0172 3.9337 3.8507 3.7683 3.6863 3.6047 3.5233 3.4422 3.3612 3.2802 3.1992 3.1181 3.0368 2.9551 2.8730 2.7903 2.7070 2.6227 2.5375 2.4511 2.3633 2.2737 2.1821 2.0882 1.8909 1.6763 1.4335 1.1379 0.6865 0 7.3549 7.2958 7.2387 7.1833 7.1296 7.0775 7.0269 6.9777 6.9299 6.8833 6.8379 6.7935 6.7502 6.7078 6.6663 6.6256 6.5857 6.5465 6.5079 6.4698 6.4323 6.3952 6.3585 6.3221 6.2861 6.2503 6.2146 6.1791 6.1437 6.1083 6.0730 6.0375 6.0019 5.9662 5.9301 5.8938 5.8571 5.8199 5.7821 5.7437 5.7045 5.6643 5.6230 5.5804 5.5362 5.4417 5.3357 5.2112 5.0526 4.7971 4.4298 82 THERMODYNAMICS ASHRAE PSYCHROMETRIC CHART NO. 1 10 20 30 40 506070809010 0 11 0 11 0 12 0 12 0 E N TH A LP Y - K J P E R K IL O G R A M O F D R Y A IR 10 20 30 40 50 60 70 80 90 10 0 EN TH AL PY - K J P ER KI LO GR AM O F D RY AI R SA TU RA TIO N TE MP ER AT UR E - °C 5 10 15 20 25 30 35 40 45 50 DRY BULB TEMPERATURE - °C .0 02 .0 04 .0 06 .0 08 .0 10 .0 12 .0 14 .0 16 .0 18 .0 20 .0 22 .0 24 .0 26 .0 28 .0 30 10 % R EL AT IV E H U M ID IT Y 20 % 30 % 40 % 50 % 60 % 70 % 80 % 90 % 5 5 10 10 15 15 20 20 25 25 30 W ET B UL B TE M PE RA TU RE - °C 30 0.78 0.80 0.82 0.84 0.86 VO LUM E - C UBIC ME TER PER KG DR Y AI R 0.88 0.90 0.92 0.94 HUMIDITY RATIO - KILOGRAMS MOISTURE PER KILOGRAM DRY AIR R R A SH R A E PS YC H R O M ET R IC C H A R T N O .1 N O R M A L TE M PE R A TU R E B A R O M ET R IC P R ES SU R E: 1 01 .3 25 k Pa C op yr ig ht 1 99 2 AM ER IC AN S O C IE TY O F H EA TI N G , R EF R IG ER AT IN G A N D A IR -C O N D IT IO N IN G E N G IN EE R S, IN C . SE A L EV EL 0 1.0 1.0 - 1.5 2.0 4.0 -4. 0 -2. 0 -1.0 -0.5 -0.2 0.1 0.2 0.3 0.4 0.5 0.60.70.8 -5 .0 -2. 0 0.0 1.0 2.0 2.5 3.0 4.0 5.0 10.0 -   SE N SI B LE H EA T Q s TO TA L H EA T Q t EN TH AL PY H U M ID IT Y R AT IO  h  W 83THERMODYNAMICS THERMAL AND PHYSICAL PROPERTY TABLES GASES cp cv Substance Mol wt kJ/(kg·K) Btu/(lbm- ° R) kJ/(kg·K) Btu/(lbm- ° R) k Gases Air Argon Butane Carbon dioxide Carbon monoxide Ethane Helium Hydrogen Methane Neon Nitrogen Octane vapor Oxygen Propane Steam 29 40 58 44 28 30 4 2 16 20 28 114 32 44 18 1.00 0.520 1.72 0.846 1.04 1.77 5.19 14.3 2.25 1.03 1.04 1.71 0.918 1.68 1.87 0.240 0.125 0.415 0.203 0.249 0.427 1.25 3.43 0.532 0.246 0.248 0.409 0.219 0.407 0.445 0.718 0.312 1.57 0.657 0.744 1.49 3.12 10.2 1.74 0.618 0.743 1.64 0.658 1.49 1.41 0.171 0.0756 0.381 0.158 0.178 0.361 0.753 2.44 0.403 0.148 0.177 0.392 0.157 0.362 0.335 1.40 1.67 1.09 1.29 1.40 1.18 1.67 1.40 1.30 1.67 1.40 1.04 1.40 1.12 1.33 0.2870 0.2081 0.1430 0.1889 0.2968 0.2765 2.0769 4.1240 0.5182 0.4119 0.2968 0.0729 0.2598 0.1885 0.4615 R kJ/(kg·K) SELECTED LIQUIDS AND SOLIDS cp Density Substance kJ/(kg·K) Btu/(lbm- ° R) kg/m 3 lbm/ft 3 Liquids Ammonia Mercury Water 4.80 0.139 4.18 1.146 0.033 1.000 602 13,560 997 38 847 62.4 Solids Aluminum Copper Ice (0°C; 32°F) Iron Lead 0.900 0.386 2.11 0.450 0.128 0.215 0.092 0.502 0.107 0.030 2,700 8,900 917 7,840 11,310 170 555 57.2 490 705