Page 177 - Modelling in Transport Phenomena A Conceptual Approach

6.3. CONSERVATION OF ENERGY 157

in which (AT),, is the characteristic temperature difference. Note that Qint is
considered positive when energy is added to the system. In a similar way, W is
also considered positive when work is done on the system.

/ Qint /

Figure 6.2 Steady-state flow system with fixed boundaries interchanging energy
in the form of heat and work with the surroundings.

As stated in Section 2.4.2, the rate of energy entering or leaving the system, E,
is expressed as
&=Em (6.3-4)
Therefore, Eq. (6.3-2) becomes

<E *)in - (Eh)out + Qint + W = o (6.3-5)

To determine the total energy per unit mass, E, consider an astronaut on the space
shuttle Atlantis. When the astronaut looks at the earth, (s)he sees that the earth
has an external kinetic energy due to its rotation and its motion around the sun.
The earth also has an internal kinetic energy as a result of all the objects, i.e.,
people, cars, planes, etc., moving on its surface which the astronaut cannot see.
A physical object is usually composed of smaller objects, each of which can have
a variety of internal and external energies. The sum of the internal and external
energies of the smaller objects is usually apparent as internal energy of the larger
objects.
The above discussion indicates that the total energy of any system is expressed
as the sum of its internal and external energies. Kinetic and potential energies
constitute the external energy, while the energy associated with the translational,
rotational, and vibrational motion of molecules and atoms is considered as the
internal energy. Therefore, total energy per unit mass can be expressed as
+
E = 6 EK + Ep (6.3-6)
where 8, EK and Ep represent internal, kinetic and potential energies per unit
mass, respectively. Substitution of Eq. (6.3-6) into Eq. (6.3-5) gives