Table 7.2.1: Constant Pressure Heat Capacities for a few Substances ...

Table 7.2.1: Constant Pressure Heat Capacities for a few Substances at 298.2 K and 1 bar.1 Cp,m (J K-1 mol-1) 20.786 20.786 29.14 37.11

Substance He (g) Xe (g) CO (g) CO2 (g)

Substance CH4 (g) C2H6 (g, ethane) C3H8 (g, propane) C4H10 (g, n-butane)

Cp,m (J K-1 mol-1) 35.309 52.63 73.51 97.45

Table 7.2.2: Constant Pressure Heat Capacities for Different Phases.2 Substance Zn Hg CO H2O C3H8 , propane

T (K) 693 1000 234 500 68 80 263 298 85 298

Solid Cp,m (J K-1 mol-1) 30. 28. 52.9 38.09 52.7

Liquid Cp,m (J K-1 mol-1) 31. 31. 28. 28. 60.2 60.7 75.291 75.291 85.

Gas Cp,m (J K-1 mol-1) 20.8 20.8 28.9 33.58 73.5

Table 7.2.3: Heat Capacity Coefficients for the Expansion: Cp,m = a + b T + c T2+ d T3 from 300 to 1800 K.3 Substance N2 (g) O2 (g) H2 (g) CO (g) CO2 (g) H2O (g) NH3 (g) CH4 (g)

a J K-1 mol-1 28.883 25.460 29.088 28.142 22.243 32.218 24.619 19.875

b 10-2 J K-2 mol-1 -0.157 1.519 -0.192 0.167 5.977 0.192 3.75 5.021

c 10-5 J K-3 mol-1 0.808 -0.715 0.400 0.537 -3.499 1.055 -0.138 1.268

d 10-9 J K-4 mol-1 -2.871 1.311 -0.870 -2.221 7.464 -3.593 – -11.004

Table 7.5.1: Van der Waals coefficients6 Molecule a (bar L2 mol-2) a (atm L2 mol-2) Helium 0.03460 0.03415 Hydrogen 0.02465 0.2432 Nitrogen 1.3661 1.3483 Oxygen 1.3820 1.3639 Water 5.536 5.464 Ethylene 4.6112 4.5509 Ethane 5.5818 5.5088 Propane 9.3919 9.2691 Benzene 18.876 18.629

b (L mol-1) 0.02373 0.02667 0.03858 0.03186 0.03049 0.05820 0.06514 0.09049 0.11974

130 120 110 100

P (bar)

90 80

liquid

vapor

70 60

B

50°C

A

35°C 30.99°C 22.4°C 15°C

50 40

2-phase region

30 Vm,liq

0

0.1

0.2

Vm,vap

0.3

V m (L)

0.4

Figure 7.5.2: Phase diagram for CO2. The two phase region is outlined by the dashed line. Table 7.5.2: Critical Constants.6 helium nitrogen oxygen water carbon dioxide propane

Pc (bar) 2.2750 34.000 50.427 220.55 73.843 42.477

Pc (atm) 2.2452 33.555 50.768 217.66 72.877 41.922

Vm,c (L mol-1) 0.05780 0.09010 0.07640 0.05595 0.09400 0.2030

Tc (K) 5.1950 126.20 154.58 647.126 304.14 369.85

Figure 7.5.3: Van der Waals isotherms for CO2. Tc = 30.99°C. Table 7.5.3: Redlich-Kwong coefficients6 Molecule A (bar L2 mol-2) A (atm L2 mol-2) Helium 0.07991 0.07886 Hydrogen 1.4333 1.4145 Nitrogen 15.551 15.348 Oxygen 17.411 17.183 Ethylene 78.512 77.486 Ethane 98.831 97.539 Propane 183.02 180.63 Benzene 453.32 447.39

Figure 7.5.4: (a) Compressibility factor for CO2

B (L mol-1) 0.01645 0.01848 0.02674 0.02208 0.04034 0.04515 0.06272 0.08300

Table 7.5.4: Virial Coefficients at 298.15K.7 Molecule Helium Hydrogen Nitrogen Oxygen

B (L mol-1) 0.0113 0.0141 -0.0045 -0.0161

C (L2 mol-2) 1.21x10-4 3.50x10-4 0.001100 0.001200

Table 7.6.1: The coefficient of thermal expansion and isothermal compressibility at 25°C. Substance Benzene Water Cu Diamond

α (K-1) 12.4x10-4 2.57x10-4 0.500x10-4 0.030 x10-4

κT (bar-1) 90.9x10-6 45.3x10-6 0.775x10-6 0.185x10-6

Table 7.9.1. Non PV-work. Type

work

change in internal energy

Surface tension

ñw = γ dσ

dU = ñq – PextdV +γ dσ

Extension

ñw = – f dl

dU = ñq – PextdV – f dl

Gravity

ñw = mg dh

dU = ñq – PextdV + mg dh

Electrical

ñw = φ dqi ñw = zi F φ dni

dU = ñq – PextdV + φ dqi dU = ñq – PextdV + zi F φ dni

Chemical

ñw = µi dni

dU = ñq – PextdV + µi dni