Chapter 2: Energy and the 1st Law of Thermodynamics
Transcript of Chapter 2: Energy and the 1st Law of Thermodynamics
Chapter 2Energy and the 1st Law of Thermodynamics
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Work and Kinetic Energy
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Potential Energy
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Conservation of Energy in Mechanics
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Broadening Our Understanding of Work
thermodynamic definition of work: Work is
done by a system on its surroundings if the
sole effect on everything external to the
system could have been the raising of a
weight.
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Modeling Expansion or
Compression Work
dVp
V
V
2
1
Work is process (path) dependent, and is NOT a property of the system
Expansion/Compression Work
(Moving Boundary Work)
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Sign Convention – Work
W > 0: Work done by the system
W < 0: Work done on the system
Power: Time rate of work
W
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Example 2.1Evaluating Expansion Work
A gas in a piston–cylinder assembly undergoes an
expansion process for which the relationship
between pressure and volume is given by
The initial pressure is 3 bar, the initial volume is 0.1 m3,
and the final volume is 0.2 m3. Determine the work
for the process, in kJ, if
a. n 1.5,
b. n 1.0, and
c. n 0.
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Further Examples of Work
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Rotating Shaft
Electric Power
Broadening Our
Understanding of Energy
Mechanical Energy: KE, PE, E
Work is done by energy transfer.
Heat is another form of energy.
Need to expand the conservation of
energy principle to accommodate
thermal systems.
Broadening Our
Understanding of EnergyIn engineering TD the change in total energy of a
system is considered to be made up of three
macroscopic contributions:
1. change in kinetic energy, associated with
motion of system as a whole relative to an
external coordinate frame.
2. change in gravitational potential energy, associated with position of the system as a whole
in the earth’s gravitational field.
3. All other energy changes are lumped together in
the internal energy of the system. internal energy is an extensive property of the system.
Common Units: J(N·m) or kJ, ft·lbf, Btu
)(2
1 2
1
2
2 VVmKE
)( 12 zzgmPE
Kinetic Energy
Potential Energy
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Broadening Our
Understanding of Energy
Total Energy: An extensive property of a
system
Kinetic Energy (Mechanical)
Potential Energy (Mechanical)
Internal Energy: U or u
Represents all other forms of energy
Includes all microscopic forms of energy
E KE PE U
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Broadening Our
Understanding of Energy
Microscopic Interpretation of Internal Energy
Consider a system consisting of a gas contained in a tank.
Think about the energy attributed to motions and configurations of
individual molecules, atoms, and subatomic particles making up the
matter in the system:
Gas molecules move about, encountering other molecules or walls of
container.
Part of internal energy of gas is translational kinetic energy of molecules.
kinetic energy due to rotation of molecules relative to their centers of
mass & kinetic energy associated with vibrational motions within
molecules.
energy is stored in chemical bonds between atoms that make up the
molecules.
Energy storage on the atomic level includes energy associated with
electron orbital states, nuclear spin, and binding forces in the nucleus.
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Sign Convention, Notation, and Heat Transfer Rate
Q > 0: Heat transfer into
the system
Q < 0: Heat transfer out of
the system
Rate of heat transfer:
Q
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Energy Transfer by Heat
Heat Transfer Modes
Conduction
Radiation
Emissivity, e, is a property of surface that
indicates how effectively the surface radiates (0< e <1.0)
s = Stefan–Boltzmann constant
x
dTQ A
dx
4
beQ ATes
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Heat Transfer Modes
Convection ( )b fcQ hA T T
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1st Law of Thermodynamics
Consider an example
system of a piston and
cylinder with an enclosed
dilute gas characterized by
P,V,T & n.
What happens to
the gas if the piston
is moved inwards?
1st Law of Thermodynamics
If the container is
insulated the
temperature will rise,
the atoms move faster
and the pressure rises.
Is there more internal
energy in the gas?
1st Law of Thermodynamics
External agent did
work in pushing the
piston inward.
W = Fd =(PA)x
W = PV
x
1st Law of Thermodynamics
Work done on the
gas equals the
change in the gases
internal energy,
W = U
x
1st Law of Thermodynamics
Let’s change the situation:
Keep the piston fixed at its original location.
Place the cylinder on a hot plate.
What happens to gas?
1st Law of Thermodynamics
Heat flows into the gas.
Atoms move faster, internal
energy increases.
Q = heat in Joules
U = change in internal
energy in Joules.
Q = U
1st Law of Thermodynamics
What if we added
heat and pushed
the piston in at the
same time?
F
1st Law of Thermodynamics
Work is done on the gas,
heat is added to the gas
and the internal energy of
the gas increases!
Q = W + U
F
1st Law of Thermodynamics
Some conventions:
For the gases perspective:
heat added is positive, heat removed is
negative.
Work done on the gas is positive, work
done by the gas is negative.
Temperature increase means internal
energy change is positive.
1st Law of Thermodynamics
Conservation of Energy: The 1st
Law of Thermodynamics
KE PE U Q W
Change in
amount of
energy
contained within
the system
during some
time interval
=
Net amount of
energy
transferred in across the
system
boundary by
heat transfer
during the time
interval
-
Net amount of
energy
transferred out across the
system
boundary by
work during the
time interval
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Alternative Forms of the Energy
Balance
Differential Form:
dE Q W
dEQ W
dt
Time Rate Form:
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Example 2 . 2Cooling a Gas in a Piston–Cylinder
Four kilograms of a certain gas is contained within a
piston–cylinder assembly. The gas undergoes a
process for which the pressure–volume relationship is
The initial pressure is 3 bar, the initial volume is 0.1 m3,
and the final volume is 0.2 m3. The change in specific
internal energy of the gas in the process is u2 - u1 = -4.6 kJ/kg. There are no significant changes in kinetic
or potential energy. Determine the net heat transfer
for the process, in kJ.
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Example 2 . 3Considering Alternative Systems
Air is contained in a vertical piston–cylinder assembly fitted with
an electrical resistor. The atmosphere exerts a pressure of 1 bar
on the top of the piston, which has a mass of 45 kg and a face
area of .09 m2. Electric current passes through the resistor, and
the volume of the air slowly increases by .045 m3 while its
pressure remains constant. The mass of the air is 0.27 kg, and its
specific internal energy increases by 42 kJ/kg. The air and piston
are at rest initially and finally. The piston–cylinder material is a
ceramic composite and thus a good insulator. Friction between
the piston and cylinder wall can be ignored, and the local
acceleration of gravity is g 9.81 m/s2. Determine the heat
transfer from the resistor to the air, in kJ, for a system consisting of
a. the air alone,
b. the air and the piston.
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Example 2 . 4Gearbox at Steady State
During steady-state operation, a gearbox receives 60 kW
through the input shaft and delivers power through the output
shaft. For the gearbox as the system, the rate of energy transfer
by convection is
where h 0.171 kW/m2 K is the heat transfer coefficient, A 1.0 m2
is the outer surface area of the gearbox, Tb = 300 K (27C) is the
temperature at the outer surface, and Tf = 293 K (20C) is the
temperature of the surrounding air away from the immediate
vicinity of the gearbox. For the gearbox, evaluate the heat
transfer rate and the power delivered through the output shaft,
each in kW.
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Example 2 . 5Silicon Chip at Steady State
A silicon chip measuring 5 mm on a side and 1 mm in
thickness is embedded in a ceramic substrate. At steady
state, the chip has an electrical power input of 0.225 W.The top surface of the chip is exposed to a coolant whose
temperature is 20C. The heat transfer coefficient for
convection between the chip and the coolant is 150
W/m2 K. If heat transfer by conduction between the chip
and the substrate is negligible, determine the surface
temperature of the chip, in C.
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Example 2 . 6Transient Operation of a Motor
The rate of heat transfer between a certain electric motor
and its surroundings varies with time as
where t is in seconds and is in kW. The shaft of the motor
rotates at a constant speed of 100 rad/s (about 955 RPM)
and applies a constant torque of 18 N.m to an external
load. The motor draws a constant electric power input equal to 2.0 kW. For the motor, plot , each in kW,
and the change in energy E, in kJ, as functions of time
from t = 0 to t = 120 s. Discuss.
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Cycle Analysis
Power Cycles Refrigeration & Heat
Pump Cycles
cycle cycle cycleE Q W cycle cycleQ W
cycle
in
W
Q
in
cycle
Q
W
out
cycle
Q
W
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Homework Assignment # 2
Problems: 1, 7, 14, 20, 30, 36,
42, 49, 56
Design and open end
problem: 2.1D
Due Wednesday 22/2/2012
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