Modern Engineering Thermodynamics

Summary 91
and
e = E/m = u + V2
2g c
+ gZ
g c
4. The definitions of the constant volume and constant pressure specific heats from Eqs. (3.15) and (3.18):
c v =
∂u
= constant volume specific heat
∂T v
and
5. The general definition of enthalpy, Eq. (3.17):
6. The general definition of quality from Eq. (3.22):
c p =
∂h
= constant pressure specific heat
∂T p
h = u + pv = specific enthalpy
x =
m g
m g + m f
= m g
m = quality
7. The definition of the specific volume of a mixture of liquid and vapor using quality, Eqs. (3.23) and (3.24):
v = ð1 − xÞv f + xv g = v f + xv fg
where v fg = v g − v f .
8. A more general definition of quality using other specific properties from Eq. (3.27):
x = v − v f
v fg
= u − u f
u fg
= h − h f
h fg
9. For incompressible materials, we have from Eqs. (3.28), (3.33), and (3.34),
ν incompressible material = ðV/mÞ incmopressible material = constant
and
ðu 2 − u 1 Þ incompressible material = cðT 2 − T 1 Þ
so that
ðh 2 − h 1 Þ incompressible material = cðT 2 − T 1 Þ + vðp 2 − p 1 Þ
10. For constant specific heat ideal gases, we have, from Eqs. (3.35),
pV = mRT = nRT
or
pv = RT
or
pv = RT
from Eq. (3.38),
ðu 2 − u 1 Þ ideal gas
= c v ðT 2 − T 1 Þ;
and, from Eq. (3.42),
ðh 2 − h 1 Þ ideal gas
= c p ðT 2 − T 1 Þ
11. For ideal gases, only the following relation, from Eq. (3.41), also holds:
c p = c v + R