Download Complete Thermodynamics Cheat Sheet and more Cheat Sheet Thermodynamics in PDF only on Docsity!
THERMODYNAMICS
PROPERTIES OF SINGLE-COMPONENT SYSTEMS
Nomenclature
- Intensive properties are independent of mass.
- Extensive properties are proportional to mass.
State Functions (properties) Absolute Pressure, P (lbf / in^2 or Pa)
Absolute Temperature, T (°R or K) Volume, V (ft^3 or m^3 ) v (^) = V m (ft 3 / lbm or m^3 / 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 (^) p (^) Th (^2) P = b^2 l
Heat Capacity at Constant Volume, c (^) v (^) Tu (^2) v = b^2 l
Quality x (applies to liquid-vapor systems at saturation) is % % &' ' & &* x = mg / ( mg + mf ) , where
m (^) g = 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 = s (^) f + xsfg
5 6 ' %% ' &
For an ideal gas, Pv = RT or PV = mRT , and P 1 v 1 /T 1 = P 2 v 2 /T 2 , 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 0 u 0 (^2) T T
b l = b^2 l =
For cold air standard, heat capacities are assumed to be constant at their room temperature values. In that case, the following are true: Δ u = cv Δ T ; Δ h = c (^) p Δ T Δ s = c (^) p ln ( T 2 /T 1 ) – R ln ( P 2 /P 1 ); and Δ s = c (^) v ln ( T 2 /T 1 ) + R ln ( v 2 /v 1 ).
For heat capacities that are temperature dependent, the value to be used in the above equations for Δ h is known as the mean heat capacity (^) ` c (^) p j and is given by
c (^) T T
c dT p
T p
T
2 1
1
2 = (^) -
Also, for constant entropy processes:
P
P
v
v T
T
P
P
T
T
v
v (^) where k c c
k kk
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
where
2
c
c c
(^2) c 2
c ^
c f
m h
m p
where P (^) c and Tc are the pressure and temperature at the critical point, respectively, and v &
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 = Δ U + Δ KE + Δ PE
where Δ KE = change in kinetic energy, and Δ PE = change in potential energy.
Energy can cross the boundary only in the form of heat or work. Work can be boundary work, w b, or other work forms (electrical work, etc.)
Work W b w^ = Wm l^ is considered positive if it is outward or
work done by the system.
Reversible boundary work is given by w b = ∫ P dv.
Special Cases of Closed Systems Constant Pressure ( ): w b = P Δ v (ideal gas) T/v = constant
Constant Volume: w b = 0 (ideal gas) T/P = constant
Isentropic (ideal gas): Pvk^ = constant w = ( P 2 v 2 – P 1 v 1 )/(1 – k ) = R ( T 2 – T 1 )/(1 – k )
Constant Temperature ( ): (ideal gas) Pv = constant w b = RT ln ( v 2 / v 1 ) = RT ln ( P 1 / P 2 )
Polytropic (ideal gas): Pvn^ = constant w = ( P 2 v 2 – P 1 v 1 )/(1 – n )
Open Thermodynamic System Mass crosses the system boundary D& L ! Pv ) done by mass entering the system. D& 6L ! 6 * w rev = – ∫ v dP + Δ ke + Δ pe
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
where
i i (^) i i e e (^) e e in net s s
R o Ro o o (^) _ i
8 B 8 B
W^ o^ net = rate of net or shaft work transfer,
m s / 'L % & &
us / ' % Q o^ = rate of heat transfer (neglecting kinetic and potential energy of the system).
Special Cases of Open Systems Constant Volume: wrev = – v ( P 2 – P 1 ) Constant Pressure: wrev = 0 Constant Temperature: (ideal gas) Pv = constant wrev = RT ln ( v 2 / v 1 ) = RT ln ( P 1 / P 2 ) Isentropic (ideal gas): Pvk^ = constant wrev = k ( P 2 v 2 – P 1 v 1 ) / (1 – k ) = k R ( T 2 – T 1 ) / (1 – k )
w (^) k k^ 1 RT 1 PP
/ rev
k k 1 12
1 = (^) - -
d
^ n
h
H
Polytropic: Pvn^ = constant wrev = n ( P 2 v 2 – P 1 v 1 ) / (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
and
where
i (^) i i e e (^) e e in out
i e
R R
R R
o o o^ o
o o
j j
m o /L 6 i and e refer to inlet and exit states of system), g = acceleration of gravity, Z = elevation, V = velocity, and W o^ = rate of work.
Special Cases of Steady-Flow Energy Equation Nozzles , Diffusers : X elevation change, no heat transfer, and no work. Single mass stream. hi (^) + Vi^2 /^2 = he (^) + Ve^2 / 2
' 44/ , h h
V V
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
Wet-bulb temperature T (^) wb is the temperature indicated by a thermometer covered by a wick saturated with liquid water and in contact with moving air.
Humid Volume : Volume of moist air / mass of dry air.
Psychrometric Chart ` ' & % ' '% Z66 temperature plotted for a value of atmospheric pressure. (See chart at end of section.)
PHASE RELATIONS
Clapeyron Equation for Phase Transitions:
dTdP^ Tv ,
h v
s where sat fg
fg fg
b l = = fg
hfg = enthalpy change for phase transitions,
vfg = volume change,
s (^) fg = entropy change,
T = absolute temperature, and
( dP/dT ) sat = slope of phase transition (e.g.,vapor-liquid) saturation line.
Clausius-Clapeyron Equation This equation results if it is assumed that (1) the volume change ( vfg ) can be replaced with the vapor volume ( vg) ,
(2) the latter can be replaced with P R T from the ideal gas law, and (3) h (^) fg is independent of the temperature ( T ).
ln PP R
h TT
T T
e
fg 1
2 1 2
d n= :^2 -^1
Gibbs Phase Rule ( non-reacting systems ) P + F = C + 2, where P = number of phases making up a system F = degrees of freedom, and C = number of components in a system
COMBUSTION PROCESSES First, the combustion equation should be written and balanced. For example, for the stoichiometric combustion of methane in oxygen:
CH 4 + 2 O 2 → CO 2 + 2 H 2 O
Combustion in Air For each mole of oxygen, there will be 3.76 moles of nitrogen. For stoichiometric combustion of methane in air:
CH 4 + 2 O 2 + 2(3.76) N 2 → CO 2 + 2 H 2 O + 7.52 N (^2)
Combustion in Excess Air The excess oxygen appears as oxygen on the right side of the combustion equation.
Incomplete Combustion Some carbon is burned to create carbon monoxide (CO).
Air-Fuel Ratio ( A/F ): A/F = mass of fuelmass of air
Stoichiometric (theoretical) air-fuel ratio is the air-fuel ratio calculated from the stoichiometric combustion equation.
Percent Theoretical Air = A F
A F
stoichiometric
actual (^) # _
_ i
i
Percent Excess Air = A F
A F A F
stoichiometric
actual - stoichiometric (^) # _
_ _ i
i i
SECOND LAW OF THERMODYNAMICS
Thermal Energy Reservoirs Δ S reservoir = Q/T reservoir, where Q is measured with respect to the reservoir.
Kelvin-Planck Statement of Second Law No heat engine can operate in a cycle while transferring heat with a single heat reservoir.
COROLLARY to Kelvin-Planck: No heat engine can have a & & ' &\ \ 6 & same reservoirs.
Clausius’ Statement of Second Law No refrigeration or heat pump cycle can operate without a net work input.
COROLLARY : No refrigerator or heat pump can have a higher COP than a Carnot Cycle refrigerator or heat pump.
VAPOR-LIQUID MIXTURES Henry’s Law at Constant Temperature At equilibrium, the partial pressure of a gas is proportional to its concentration in a liquid. Henry’s Law is valid for low concentrations; i.e., x ≈ 0. Pi = Pyi = hxi, where h = Henry’s Law constant, P (^) i = partial pressure of a gas in contact with a liquid, x (^) i = mol fraction of the gas in the liquid, y (^) i = mol fraction of the gas in the vapor, and P = total pressure.
Raoult’s Law for Vapor-Liquid Equilibrium Valid for concentrations near 1; i.e., x (^) i ≈1. Pi = xi Pi* , where Pi = partial pressure of component i , xi = mol fraction of component i in the liquid, and P (^) i*^ = vapor pressure of pure component i at the temperature of the mixture.
ENTROPY
ds T Q s s T Q
rev rev
d d
_ _
i
i
Inequality of Clausius
T Q
T Q s s
rev #
-
d
d
_ _
i
i
Isothermal, Reversible Process Δ s = s 2 – s 1 = Q/T
Isentropic Process Δ s = 0 ; ds = 0 A reversible adiabatic process is isentropic.
Adiabatic Process δ Q = 0 ; Δ s ≥ 0
Increase of Entropy Principle
s s s s m s m s Q T
total system surroundings total out out in in external external
D D D
D o R o R o R_^ o i
Temperature-Entropy ( T-s ) Diagram
2 Q (^) rev 1 Tds
s
1
2
AREA = HEAT
T
Entropy Change for Solids and Liquids ds = c (dT/T) s 2 – s 1 = ∫ c (dT/T) = c meanln ( T 2 /T 1 ) , where c equals the heat capacity of the solid or liquid.
Irreversibility I = w rev – w actual
EXERGY
Exergy is the portion of total energy available to do work.
Closed-System Exergy (Availability) (no chemical reactions) φ = ( u – u o) – T o ( s – s o) + p o ( v – v o ) where the subscript o designates environmental conditions w reversible = φ 1 – φ 2
Open-System Exergy (Availability) ψ = ( h – h o) – T o ( s – s o) + V^2 /2 + gz w reversible = ψ 1 – ψ 2
Gibbs Free Energy, Δ G Energy released or absorbed in a reaction occurring reversibly at constant pressure and temperature.
Helmholtz Free Energy, Δ A Energy released or absorbed in a reaction occurring reversibly at constant volume and temperature.
STEAM TABLES
Saturated Water - Temperature Table Specific Volume m^3 /kg
Internal Energy kJ/kg
Enthalpy kJ/kg
Entropy Temp. kJ/(kg·K) oC T
Sat. Press. kPa p (^) sat
Sat. liquid v (^) f
Sat. vapor v (^) g
Sat. liquid u (^) f
Evap. u (^) fg
Sat. vapor u (^) g
Sat. liquid h (^) f
Evap. h (^) fg
Sat. vapor h (^) g
Sat. liquid sf
Evap. sfg
Sat. vapor
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
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
Superheated Water Tables v m^3 /kg u kJ/kg h kJ/kg s kJ/(kg ⋅ K) v m^3 /kg u kJ/kg h kJ/kg s kJ/(kg ⋅ K) T Temp.o C p (^) = 0.01 MPa (45.81oC) p (^) = 0.05 MPa (81.33oC) Sat. 50 100 150 200 250 300 400 500 600 700 800 900 1000 1100 1200 p (^) = 0.10 MPa (99.63oC) p (^) = 0.20 MPa (120.23oC) Sat. 100 150 200 250 300 400 500 600 700 800 900 1000 1100 1200 p (^) = 0.40 MPa (143.63o^ C) p (^) = 0.60 MPa (158.85oC) Sat. 150 200 250 300 350 400 500 600 700 800 900 1000 1100 1200 p (^) = 0.80 MPa (170.43o^ C) p (^) = 1.00 MPa (179.91oC) Sat. 200 250 300 350 400 500 600 700 800 900 1000 1100 1200
- sg
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0.001
- 0. - 20. - 42. - 62. - 83.
- - 2375. - 2361. - 2347. - 2333. - 2319. - 2304. - 2290. - 2276. - 2262. - 2248. - 2234. - 2219. - 2205. - 2191. - 2176. - 2162. - 2147. - 2132. - 2117. - 2102. - 2375. - 2382. - 2389. - 2396. - 2402. - 2409. - 2416. - 2423. - 2430. - 2436. - 2443. - 2450. - 2456. - 2463. - 2569. - 2475. - 2482. - 2488. - 2494. - 2500. - 0. - 20. - 42. - 62. - 83. - 104. - 125. - 146. - 167. - 188. - 209. - 230. - 251. - 272. - 292. - 313. - 334. - 355. - 376. - 397. - 2501. - 2489. - 2477. - 2465. - 2454. - 2442. - 2430. - 2418. - 2406. - 2394. - 2382. - 2370. - 2358. - 2346. - 2333. - 2321. - 2308. - 2296. - 2283. - 2270. - 2501. - 2510. - 2519. - 2528. - 2538. - 2547. - 2556. - 2565. - 2574. - 2583. - 2592. - 2600. - 2609. - 2618. - 2626. - 2635. - 2643. - 2651. - 2660. - 2668. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 1. - 1. - 1. - 9. - 8. - 8. - 8. - 8. - 8. - 8. - 7. - 7. - 7. - 7. - 7. - 7. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 9. - 9. - 8. - 8. - 8. - 8. - 8. - 8. - 8. - 8. - 8. - 7. - 7. - 7. - 7. - 7. - 7. - 7. - 7. - 7. - 374. - 0.101 - 0.120 - 0.143 - 0.169 - 0.198 - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 2. - 2. - 2. - 2. - 3. - 3. - 3. - 3. - 4. - 4. - 5. - 5. - 5. - 6. - 6. - 7. - 7. - 8. - 9. - 9. - 10. - 11. - 12. - 14. - 16. - 18. - 21. - 22. - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.001 - 0.002 - 0.003 - 1. - 1. - 1. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0.194 - 0.174 - 0.156 - 0.141 - 0.127 - 0.115 - 0.104 - 0.094 - 0.086 - 0.078 - 0.071 - 0.065 - 0.059 - 0.054 - 0.050 - 0.045 - 0.042 - 0.038 - 0.035 - 0.032 - 0.030 - 0.027 - 0.025 - 0.023 - 0.021 - 0.019 - 0.018 - 0.016 - 0.015 - 0.012 - 0.010 - 0.008 - 0.006 - 0.004 - 0.003 - 418. - 440. - 461. - 482. - 503. - 524. - 546. - 567. - 588. - 610. - 631. - 653. - 674. - 696. - 718. - 740. - 762. - 784. - 806. - 828. - 850. - 873. - 895. - 918. - 940. - 963. - 986. - 1009. - 1033. - 1056. - 1080. - 1104. - 1128. - 1152. - 1177. - 1202. - 1227. - 1253. - 1278. - 1305. - 1332. - 1359. - 1387. - 1415. - 1444. - 1505. - 1570. - 1641. - 1725. - 1844. - 2029. - 2087. - 2072. - 2057. - 2041. - 2025. - 2009. - 1993. - 1977. - 1961. - 1944. - 1927. - 1910. - 1893. - 1876. - 1858. - 1840. - 1821. - 1802. - 1783. - 1764. - 1744. - 1724. - 1703. - 1682. - 1661. - 1639. - 1617. - 1594. - 1570. - 1546. - 1522. - 1596. - 1470. - 1443. - 1416. - 1387. - 1358. - 1328. - 1297. - 1264. - 1231. - 1195. - 1159. - 1121. - 1080. - 993. - 894. - 776. - 626. - 384. - 2506. - 2512. - 2518. - 2523. - 2529. - 2534. - 2539. - 2545. - 2550. - 2554. - 2559. - 2564. - 2568. - 2572. - 2576. - 2580. - 2583. - 2587. - 2590. - 2592. - 2595. - 2597. - 2599. - 2601. - 2602. - 2603. - 2603. - 2604. - 2604. - 2603. - 2602. - 2600. - 2599. - 2596. - 2593. - 2590. - 2586. - 2581. - 2576. - 2569. - 2563. - 2555. - 2546. - 2536. - 2525. - 2498. - 2464. - 2418. - 2351. - 2228. - 2029. - 419. - 440. - 461. - 482. - 503. - 524. - 546. - 567. - 589. - 610. - 632. - 653. - 675. - 697. - 719. - 741. - 763. - 785. - 807. - 829. - 852. - 875. - 897. - 920. - 943. - 966. - 990. - 1013. - 1037. - 1061. - 1085. - 1109. - 1134. - 1159. - 1184. - 1210. - 1235. - 1262. - 1289. - 1316. - 1344. - 1372. - 1401. - 1431. - 1461. - 1525. - 1594. - 1670. - 1760. - 1890. - 2099. - 2257. - 2243. - 2230. - 2216. - 2202. - 2188. - 2174. - 2159. - 2144. - 2129. - 2114. - 2098. - 2082. - 2066. - 2049. - 2032. - 2015. - 1997. - 1978. - 1960. - 1940. - 1921. - 1900. - 1879. - 1858. - 1836. - 1813. - 1790. - 1766. - 1741. - 1716. - 1689. - 1662. - 1634. - 1605. - 1574. - 1543. - 1511. - 1477. - 1441. - 1404. - 1366. - 1326. - 1283. - 1238. - 1140. - 1027. - 893. - 720. - 441. - 2676. - 2683. - 2691. - 2699. - 2706. - 2713. - 2720. - 2727. - 2733. - 2740. - 2746. - 2752. - 2758. - 2763. - 2768. - 2773. - 2778. - 2782. - 2786. - 2790. - 2793. - 2796. - 2798. - 2800. - 2802. - 2803. - 2804. - 2804. - 2803. - 2803. - 2801. - 2799. - 2796. - 2793. - 2789. - 2785. - 2779. - 2773. - 2766. - 2758. - 2749. - 2738. - 2727. - 2714. - 2700. - 2665. - 2622. - 2563. - 2481. - 2332. - 2099. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 4. - 4. - 6. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 4. - 4. - 4. - 4. - 4. - 4. - 4. - 4. - 4. - 4. - 4. - 4. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 3. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 1. - 1. - 1. - 1. - 0. - 7. - 7. - 7. - 7. - 7. - 7. - 7. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 6. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 4. - 4. - 14. - 14. - 17. - 19. - 21. - 24. - 26. - 31. - 35. - 40. - 44. - 49. - 54. - 58. - 63. - 67. - 72. - 2437. - 2443. - 2515. - 2587. - 2661. - 2736. - 2812. - 2968. - 3132. - 3302. - 3479. - 3663. - 3855. - 4053. - 4257. - 4467. - 4683. - 2584. - 2592. - 2687. - 2783. - 2879. - 2977. - 3076. - 3279. - 3489. - 3705. - 3928. - 4159. - 4396. - 4640. - 4891. - 5147. - 5409. - 8. - 8. - 8. - 8. - 8. - 9. - 9. - 9. - 9. - 10. - 10. - 10. - 10. - 11. - 11. - 11. - 11. - 3. - 3. - 3. - 4. - 4. - 5. - 6. - 7. - 8. - 8. - 9. - 10. - 11. - 12. - 13. - 14. - 2483. - 2511. - 2585. - 2659. - 2735. - 2811. - 2968. - 3132. - 3302. - 3479. - 3663. - 3854. - 4052. - 4257. - 4467. - 4683. - 2645. - 2682. - 2780. - 2877. - 2976. - 3075. - 3278. - 3488. - 3705. - 3928. - 4158. - 4396. - 4640. - 4891. - 5147. - 5409. - 7. - 7. - 7. - 8. - 8. - 8. - 8. - 9. - 9. - 9. - 9. - 10. - 10. - 10. - 10. - 10. - 1. - 1. - 1. - 2. - 2. - 2. - 3. - 3. - 4. - 4. - 4. - 5. - 5. - 6. - 6. - 7. - 2506. - 2506. - 2582. - 2658. - 2733. - 2810. - 2967. - 3131. - 3301. - 3479. - 3663. - 3854. - 4052. - 4257. - 4467. - 4683. - 2675. - 2676. - 2776. - 2875. - 2974. - 3074. - 3278. - 3488. - 3704. - 3928. - 4158. - 4396. - 4640. - 4891. - 5147. - 5409. - 7. - 7. - 7. - 7. - 8. - 8. - 8. - 8. - 9. - 9. - 9. - 9. - 9. - 10. - 10. - 10. - 0. - 0. - 1. - 1. - 1. - 1. - 1. - 2. - 2. - 2. - 2. - 2. - 3. - 3. - 3. - 2529. - 2576. - 2654. - 2731. - 2808. - 2966. - 3130. - 3301. - 3478. - 3663. - 3854. - 4052. - 4257. - 4467. - 4683. - 2706. - 2768. - 2870. - 2971. - 3071. - 3276. - 3487. - 3704. - 3927. - 4158. - 4395. - 4640. - 4890. - 5147. - 5409. - 7. - 7. - 7. - 7. - 7. - 8. - 8. - 8. - 9. - 9. - 9. - 9. - 9. - 10. - 10. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 2553. - 2564. - 2646. - 2726. - 2804. - 2964. - 3129. - 3300. - 3477. - 3662. - 3853. - 4052. - 4256. - 4467. - 4682. - 2738. - 2752. - 2860. - 2964. - 3066. - 3273. - 3484. - 3702. - 3926. - 4157. - 4395. - 4639. - 4890. - 5146. - 5408. - 6. - 6. - 7. - 7. - 7. - 7. - 8. - 8. - 8. - 8. - 9. - 9. - 9. - 9. - 9. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 1. - 2567. - 2638. - 2720. - 2801. - 2881. - 2962. - 3127. - 3299. - 3477. - 3661. - 3853. - 4051. - 4256. - 4466. - 4682. - 2756. - 2850. - 2957. - 3061. - 3165. - 3270. - 3482. - 3700. - 3925. - 4156. - 4394. - 4638. - 4889. - 5146. - 5408. - 6. - 6. - 7. - 7. - 7. - 7. - 8. - 8. - 8. - 8. - 8. - 9. - 9. - 9. - 9. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 2576. - 2630. - 2715. - 2797. - 2878. - 2959. - 3126. - 3297. - 3476. - 3661. - 3852. - 4051. - 4255. - 4466. - 4681. - 2769. - 2839. - 2950. - 3056. - 3161. - 3267. - 3480. - 3699. - 3924. - 4155. - 4393. - 4638. - 4889. - 5145. - 5407. - 6. - 6. - 7. - 7. - 7. - 7. - 7. - 8. - 8. - 8. - 8. - 9. - 9. - 9. - 9. - 0.194 - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 2583. - 2621. - 2709. - 2793. - 2875. - 2957. - 3124. - 3296. - 3475. - 3660. - 3852. - 4050. - 4255. - 4465. - 4681. - 2778. - 2827. - 2942. - 3051. - 3157. - 3263. - 3478. - 3697. - 3923. - 4154. - 4392. - 4637. - 4888. - 5145. - 5407. - 6. - 6. - 6. - 7. - 7. - 7. - 7. - 8. - 8. - 8. - 8. - 8. - 9. - 9. - 9. - 0.7137 2884.6 3170.1 7.
ASHRAE PSYCHROMETRIC CHART NO. 1
METRIC UNITS
2EPRODUCED BY PERMISSION OF !3(2!%
10
20
30
40
110 100 90 80 70 60 50
110
120
120 ENTHALPY - KJ PER KILOGRAM OF DRY AIR
10
20
30
40
50
60
70
80
90
100
ENTHALPY - KJ PER KILOGRAM OF DRY AIR
SATURATION TEMPERATURE - °C
5
10
15
20
25
30
35
40
45
50
DRY BULB TEMPERATURE - °C
.030 .028 .026 .024 .022 .020 .018 .016 .014 .012 .010 .008 .006 .004.
90% 80% 70% 60% 50% 40% 30% 20% 10% RELATIVE HUMIDITY
5
5
10
10
15
15
20
20
25
25
30 WET BULB TEMPERATURE - °C
30
0.86 VOLUME - CUBIC METER PER KG DRY AIR
HUMIDITY RATIO - KILOGRAMS MOISTURE PER KILOGRAM DRY AIR
R^
R
ASHRAE PSYCHROMETRIC CHART NO.
NORMAL TEMPERATURE
BAROMETRIC PRESSURE: 101.325 kPa
Copyright 1992
AMERICAN SOCIETY OF HEATING, REFRIGERATING AND AIR-CONDITIONING ENGINEERS, INC.
SEA LEVEL
0
1.^
1. -
1.52.04. -4.0-2. -1. -0. -0.
0. (^) **0.
0.60. 0.80.**
**-5.0-2.
1.**
2.
2.
3.
**4.
10.**
-
SENSIBLE HEAT
Qs
TOTAL HEAT
Qt
ENTHALPY HUMIDITY RATIO
h W
THERMAL AND PHYSICAL PROPERTY TABLES
AT ROOM TEMPERATURE
GASES cp cv Substance Molwt 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
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
Solids
Aluminum Copper Ice (0°C; 32°F) Iron Lead
