Page 25 - Advanced thermodynamics for engineers

8 CHAPTER 1 INTRODUCTION AND REVISION

The change of internal energy, dE, of a system of mass, m,is
V 2 2 V 1 2
E 2 E 1 ¼ m m þ mgh 2 mgh 1 þ mu 2 mu 1 (1.8)
2 2
which is made up of three components:
V 2 2 V 1 2
dðKEÞ¼ m m ; (1.9)
2 2
dðPEÞ¼ mgh 2 mgh 1 ; (1.10)
and
change of thermal energy ¼ mu 2 mu 1 : (1.11)
The thermal energy (u), which is based solely on the thermodynamic properties of the system, is
termed the specific intrinsic internal energy. The total energy of a moving system in a gravitational
field is given by

V 2 2 V 1 2
E 2 E 1 ¼ m m þ mgh 2 mgh 1 þ mu 2 mu 1 (1.12)
2 2
and hence, applying the First Law (Eqn (1.7)), the net transfer of work and heat is

2 2
V 2 V 1
dQ dW ¼ m u 2 þ þ gh 2 m u 1 þ þ gh 1 : (1.13)
2 2

1.5.5.4 Intrinsic internal energy, U or u
The intrinsic internal energy is the energy of the system based on the molecular motion inside the
system. It obeys the two-property rule, and is hence a function of any two independent properties.
The specific intrinsic internal energy is a specific property, defined by

u ¼ uðT; vÞ
u ¼ uðp; TÞ; etc: (1.14)

and the intrinsic internal energy
U ¼ Uðm; T; vÞ
U ¼ Uðm; p; TÞ; etc: (1.15)
The intrinsic internal energy is an extensive property.

1.5.5.5 Specific heat at constant volume, c v
The specific heat at constant volume is a useful concept for single-phase pure substances. The specific
heat at constant volume is defined as the rate of change of specific intrinsic internal energy at constant
volume with temperature. This may be written mathematically as

vu vu vQ
c v ¼ ¼ ¼ : (1.16)
vT v vt v vT v