Modern Engineering Thermodynamics

78 CHAPTER 3: Thermodynamic Properties
since for incompressible materials v =constant and β = 0. However, note that, since β is very small for most
liquids and solids (see Tables 3.1 and 3.2), these substances can be accurately modelled as incompressible materials.
The subscripts p and v are meaningless for an incompressible material, and the simple phrase specific heat,
represented by the symbol c with no subscript, is sufficient. Thus, for all incompressible substances, c p = c υ = c.
Consequently, for these materials, we can write
Z T2
u 2 − u 1 = cdT (3.32)
T 1
and if c is constant over the temperature range from T 1 to T 2 , then Eq. (3.32) becomes
Also, since v 2 = v 1 = v here,
u 2 − u 1 = cT ð 2 − T 1 Þ (3.33)
h 2 − h 1 = cT ð 2 − T 1 Þ + vp ð 2 − p 1 Þ (3.34)
Tables 3.5 and 3.6 list the specific heats of some materials whose liquid and solid phases accurately approximate
incompressible substances.
Table 3.5 Specific Heats of Various Liquids at Atmospheric Pressure
T
c
Substance R K Btu/lbm · R kJ/kg · K
Benzene 520. 289 0.430 1.800
Butane (n) 492 273 0.550 2.303
Glycerin 510. 283 0.576 2.320
Mercury 510. 283 0.033 0.138
Propane 492 273 0.576 2.412
Water 492 273 1.007 4.186
Source: Some material drawn from Wark, K., Jr. 1988. Thermodynamics, fifth ed. McGraw-Hill, New York. Reprinted by permission of the publisher.
Table 3.6 Specific Heats of Various Solids at Atmospheric Pressure
T
c
Substance R K Btu/lbm · R kJ/kg · K
Aluminum 360. 200. 0.190 0.797
540. 300. 0.215 0.902
720. 400. 0.227 0.949
900. 500. 0.238 0.997
Copper 540. 300. 0.092 0.386
851 473 0.096 0.403
Graphite 527 293 0.170 0.712
Iron 527 293 0.107 0.448
Lead 540. 300. 0.031 0.129
851 473 0.032 0.136
Rubber 527 293 0.439 1.84
Silver 527 293 0.056 0.233
Water (ice) 492 273 0.504 2.11
Wood 527 293 0.420 1.76
Source: Excerpted from Wark, K., Jr. 1988. Thermodynamics, fifth ed. McGraw-Hill, New York. Reprinted by permission of the publisher.