Thermodynamics I
Spring 1432/1433H (2011/2012H)
Saturday, Wednesday 8:00am - 10:00am &
Monday 8:00am - 9:00am MEP 261 Class ZA
Dr. Walid A. Aissa Dr. Walid A. Aissa
Associate Professor, Mech. Engg. Dept.
Faculty of Engineering at Rabigh, KAU, KSA Chapter #2
April XX, 2012
2–2 ■ FORMS OF ENERGY
(2-2)
kinetic energy per unit mass (
ke
) isPotential energy per unit mass (
pe
) is(2-4)
(2-5)
and per unit mass (2-6)
(2-7)
The change in the total energy; ∆E of a
stationary system is identical to the change in its internal energy; ∆U. In this text, a
closed system is assumed to be stationary unless stated otherwise.
0 0
From Eq. (2-6):
(2-6b)
0 0
which is analogous to
(2-8)
The energy flow rate associated with a fluid flowing at a rate of , is
fluid flowing at a rate of , is
which is analogous to E = me.
(2-9)
M.E. of a flowing fluid can be expressed on a unit mass basis as:
flow energy (F.E.) P.E.
(2-10)
flow energy (F.E.)
K.E. P.E.
It can also be expressed in rate form as
(2-11)
Where is the mass flow rate of the fluid. Then the mechanical energy change of a fluid during incompressible (ρ = constant) flow becomes
(2-12) (2-12)
(2-13)
The amount of heat transferred during the
process between two states (states 1 and 2) is denoted by Q12, or just Q. Heat transfer per unit
mass of a system is denoted q and is determined from:
(2-14) (2-14) Heat transfer rate ( )is defined as the
amount of heat transferred per unit time.
When varies with time, the amount of heat transfer during a process is determined by:
(2-15)
When remains constant during a process, When remains constant during a process, this relation reduces to:
(2-16)
where ∆
t = t
2- t
1is the time interval during
which the process takes place.
2–4 ■ ENERGY TRANSFER BY WORK
The work done per unit mass of a
system is denoted byw and is expressed as
Work done
per unit time is called power and is denoted .
The unit of power is kJ/s, or kW.Heat and work r
directional quantities. Complete
description of a heat or work interactionrequires the specification of both the
magnitude
anddirection.
and
direction.
Sign convention for heat and work
Heat transfer to a system and work done by a system r +ve; heat transfer from a
system and work done on a system r -ve.
Electrical Work
The electrical power is,
(2-18)
Electrical power in terms of resistance
R, current I, and
potential difference V.
The electrical work done during a time interval ∆∆∆∆t is expressed as
When both V and
I remain constant during
∆∆
∆∆
(2-19)
the time interval ∆
∆∆∆t, it reduces to(2-20)
2–5 ■ MECHANICAL FORMS OF WORK
Work done is proportional to the force applied (
F)
Work done is proportional to the force applied (F) and the distance
traveled (s).
(2-21)
(2-22)
If the force F is not constant, the work
done is obtained by adding (i.e., integrating
) the differential amounts of work, .
(2-22)
Shaft Work
Power transmitted through the shaft is expressed as
′′′′
where, (rad/s)
N in rpm
(2-26′′′′) (kW)
(2- #1)
When a force;
F
is applied on a spring, the length of the spring changes by a differential amountdx, the work done is
work done is
For linear elastic springs, the displacement
x is proportional to the force applied. i.e.,
(2-27)
(2-28)
where x
1and x
2r the initial and the final displacements of the spring, respectively.
(2-29)
Power Required to Raise or to Accelerate a Body
(2- #2)
(2- #3)
Energy Balance
Change in the total energy of the system
Total energy leaving the
system
=
Total energy entering the system
-
∆
∆
∆ ∆E = E
in– E
outEnergy Change of a System, ∆ ∆ ∆ ∆E
systemEnergy change
Energy at final state
Energy at initial state
= -
∆E
system= E
final- E
initial= E
2– E
1(2-32)
∆E = ∆U + ∆KE + ∆PE
(2-33) where
∆U = m (u
2– u
1) ∆KE = ½ m (V
22– V
12)
∆PE = mg (z
2– z
1)
LHS RHS
RHS
Most systems encountered in practice r
stationary, i.e., they do not involve any changes in their velocity or elevation during a process
For stationary
systems, ∆KE = ∆PE
= 0; thus ∆ E = ∆ U.
RHS
Mechanisms of Energy Transfer, E
in& E
outEnergy can be transferred to or from a
system in three forms:
heat, work,
andmass flow
1. Heat Transfer,
Q
2. Work Transfer,W
3. Mass Flow,3. Mass Flow,
E
in- E
out= (Q
in- Q
out)+ (W
in- W
out) +(E
mass,in- E
mass,out)= ∆E
system(2-34) LHS
RHS
Energy content of a C.V. can be changed by mass flow as well as heat and work
interactions.
1) Heat transfer; Q = 0 (for adiabatic systems)
Special cases:
2) Work transfer; W = 0 (for systems that involve no work interactions)
3) Energy transport with mass; E
mass = 0(for 3) Energy transport with mass; E
mass = 0(for systems that involve no mass transfer:
Closed systems)
Eq. (2-34) can be re-written as
E in - E out = ∆E system
Net energy transfer
(kJ)
Change in
internal, kinetic, transfer
by heat, work
& mass
internal, kinetic, potential, etc,
energies
(2-35)
LHS RHS
Or, in the rate form, as
(kW)
(2-36)
LHS RHS
For constant rates, the total quantities during a time interval ∆ t are related to
the quantities per unit time as
and (kJ) (2-37)
and (kJ)
The energy balance can be expressed on a per unit mass basis as
(2-37)
e
in- e
out= ∆ ∆ ∆e ∆
system(kJ/kg) (2-38)
For closed system undergoing a cycle:
From Eq. (2-34)
∆E
system= E
in- E
out=
= (Q
in- Q
out)+ (W
in- W
out)
+ (E - E )
0 0
+ (E
mass,in- E
mass,out)
0 0
Hence, Energy Eq. can be put in the following form:
(Q
out– Q
in) = (W
in- W
out)
(2-40)
or
