Page 78 - Coulson Richardson's Chemical Engineering Vol.6 Chemical Engineering Design 4th Edition

FUNDAMENTALS OF ENERGY BALANCES
Energy can exist in many forms and this, to some extent, makes an energy balance
more complex than a material balance. 61
3.3. FORMS OF ENERGY (PER UNIT MASS OF MATERIAL)

3.3.1. Potential energy
Energy due to position:
Potential energy D gz 3.1
where z D height above some arbitrary datum, m,
2
g D gravitational acceleration (9.81 m/s ).

3.3.2. Kinetic energy
Energy due to motion:
u 2
Kinetic energy D 3.2
2
where u D velocity, m/s.

3.3.3. Internal energy

The energy associated with molecular motion. The temperature T of a material is a
measure of its internal energy U:
U D f T 3.3

3.3.4. Work
Work is done when a force acts through a distance:
1

W D F dx 3.4
0
where F D force, N,
x and l D distance, m.
Work done on a system by its surroundings is conventionally taken as negative; work
done by the system on the surroundings as positive.
Where the work arises from a change in pressure or volume:
2
W D P dv 3.5
1
2
where P D pressure, Pa (N/m ),
3
v D volume per unit mass, m /kg.
To integrate this function the relationship between pressure and volume must be known.
In process design an estimate of the work done in compressing or expanding a gas is