PA
F
ext
A
dV
dl
/
•
If non-flow piston moves slowly the external force and the
differential distance moved by piston in cylinder are:
•
Substitute and cancel out the cross-
sectional area “A”.
Express either as extensive or intensive quantities:
(kJ)
PdV
dW
(kJ/kg)
Pdv
dw
Work is positive into system and negative out of system. The
negative sign maintains the sign convention

© Heriot-Watt University
15
Heat Capacity
The heat capacity is the amount of energy a substance can
store per unit mass (or mole) per unit temperature rise:
V
V
T
u
C
•
Heat Capacity of Constant Volume:
Increase in internal energy for small change in
temperature
–
keep volume constant
–
•
Heat Capacity of Constant Pressure:
P
P
T
h
C
Increase in enthalpy for small change in
temperature
–
keep pressure constant
–
The heat capacity may be specific (kJ/kg K) or may be molar
(kJ/kmol K)
–
thus “u” or “h” may be specific (kJ/kg) or molar
(kJ/kmol). The units must be consistent.

© Heriot-Watt University
16
Internal Energy and Enthalpy
Internal energy:
“u” is the total kinetic and potential energy
of all the molecules in a system.
•
It depends on the T & P of a substance.
•
It can be both specific “u” (kJ/kg) or molar “u” (kJ/kmol).
•
It is an energy storage term
–
a thermodynamic property.
Enthalpy:
“h” is an auxiliary property of internal energy
- it
includes the additional “pressure energy” term “Pv”.
•
It too depends on the T & P of a substance.
•
It too can be specific “h” (kJ/kg) or molar “h” (kJ/kmol).
•
It too is an energy storage term
–
a thermodynamic
property. It is linked to internal energy through definition:
Pv
u
h

© Heriot-Watt University
17
1.2 Non-Flow Processes
1.
Constant Volume Process:
If volume is constant then boundary is rigid and fixed, no
work can be done if boundary cannot move.
)
(J
Q
Only heat may enter or leave the
system:
•
Heat in is positive.
•
Heat out is negative
1
2
u
u
q
•
The non-flow energy equation then simply reduces to
either intensive or extensive forms:
1
2
u
u
m
Q
Or,

© Heriot-Watt University
18
dT
du
C
V
dT
C
du
V
dT
C
u
u
T
T
V
2
1
1
2
dT
C
q
T
T
V
2
1
Constant Volume Heat Balance
For an ideal-
gas internal energy “u” is a function of
temperature only (independent of pressure) - thus
•
Integrating left and right leads to
•
Substitute result back into
non-flow expression yields
dT
C
m
Q
T
T
V
2
1
Or,

© Heriot-Watt University
19
Non-Flow Processes
2.
Constant Pressure Process:
In this case the boundary moves, so both heat and work
may be transferred.
For a constant pressure process the non-flow expressions are:
•
Heat and work transferred to
system is positive.
•
Heat and work transferred
from system is negative
)
(J
Q
)
(J
W
1
2
v
v
P
w
1
2
h
h
q

© Heriot-Watt University
20
dT
dh
C
P
dT
C
dh
P
dT
C
h
h
T
T
P
2
1
1
2
dT
C
q
T
T
P
2
1
Constant Pressure Heat Balance
For an ideal-
gas internal energy “h” is also a function of
temperature only (independent of pressure) - thus
•
Integrating left and right leads to
•
Substitute result back into
non-flow expression gives
dT
C
m
Q
T
T
P
2
1
Or,

© Heriot-Watt University
21
Constant Volume Heat Balance Summary

#### You've reached the end of your free preview.

Want to read all 58 pages?

- Winter '18
- Kathiresvaran
- Thermodynamics, Energy, Heriot-Watt University