ME 200 L4: Energy in Transition: Work and Heat
Spring 2014 MWF 1030-1120 AM
J. P. Gore, Reilly University Chair Professor
gore@purdue.edu
Gatewood Wing 3166, 765 494 0061
Office Hours: MWF 1130-1230
TAs: Robert Kapaku rkapaku@purdue.edu
Dong Han han193@purdue.edu
Resources for our learning
• Fundamentals of Engineering Thermodynamics, Moran,
Shapiro, Boettner and Bailey, Seventh Edition.
• Read assigned sections before coming to class.
• Group class email will be used frequently to
communicate. Also use http://www.purdue.edu/mixable
• Class participation welcome and essential.
• Given the size of the class, smaller groups of ~10
students to be formed soon. Special opportunities
offered to individual ME200 Peer Mentor to lead a group.
• Other Instructors, T. A. s, Classmates, Organized
Learning Groups such as www.purdue.edu/si
• Homework: Submission, grading, and return policies will
be announced in the class.
Example Problem
• Given: A gas in a Piston-Cylinder device undergoes a polytropic
process pv1.3=const. from P1=60 lbf/in2 (or 413.69 kPa) and v1= 6 ft3/lbm
(0.3746 m3/kg) to P2=20 lbf/in2 (or 137.896 kPa)
• Find: Work done by the gas and v2 and work done on the
atmosphere if its pressure is at 14 lbf/in2
• System: Piston cylinder device
• Assumptions: Polytropic process, constant mass.
Derive the expression for 1W2 for the polytropic process
 n 1


const.
v
n
)dv  const. v dv  const. 
1W2   pdv   (

n
v
 n  1
1
1
1
2
2
2
 n 1
 n 1
 v2  n 1 
 v1 n 1 




v
v
n
n
2
1
const. 
 const. 
 P2v2 
 Pv
1 1 





n

1

n

1

n

1

n

1








 v2 n v2  n 1 
 v1n v1 n 1  P2v2  Pv
1 1
 P2 

P

1



n

1

n

1
1 n




Work done by the gas as it depressurizes
P2 v2  Pv
1 1
w
1 n
(20(13.97)  60(6)) lbf ft 3
144(in2 / ft 2 )
w
 2

0.3
in lbm 778(lbf  ft / Btu )
 49.73 Btu / lbm
Work done on the atmosphere as the gas depressurizes
2
2
1
1
watm   patm dv  patm  dv  patm (vatm 2  vatm1 )
lbf ft 3
144 (in 2 / ft 2 )
 patm (vg 2  vg1 )  14.0(13.97  6) 2 

in lbm 778(lbf  ft / Btu )
 20.65 btu / lbm;
Work done on connecting rod  49.73  20.65  29.08Btu / lbm
Energy Transfer by Heat
►The symbol Q denotes energy transferred across
the boundary of a system because of a temperature
Note the dot
difference also known as heat transfer.
The rate of energy transfer by heat = Q
►Q > 0, Q > 0 to the system
►Q < 0, Q < 0 from the system
► Q = 0, Q = 0 adiabatic
►Any energy transfer that is not because of a DT
is defined as Work (W).
Heat Transfer by Conduction
►Conduction is the transfer of energy from more
energetic particles of a substance to less energetic
adjacent particles due to interactions between them.
Always in direction of decreasing temperature.
►The time rate of energy transfer by conduction is
quantified by Fourier’s law.
►Example problem: Heat transfer through a window:
dT
Qx   A
(Eq. 2.31)
dx
Material property   1.7 W / m.K
A=0.5 m x 1.2 m;DT  15 K ; Dx  0.0254 m
15
Qx  1.7(0.6)
 602.36 W
0.0254
• Winter time shown
where outdoors is cooler
than indoors.
• Summer time, the is DT
reversed and so is the
sign of Qx
Thermal Radiation
►Net radiation exchange
between a surface at Tb and a
surface at Ts (< Tb) is shown at
right.
Black surface at
400K; > 1 m2
Hot surface, 1000K, 1 m2
►Net energy is transferred in the direction of the arrow and
quantified by
4
4
Qe  es A[Tb  Ts ]
(Eq. 2.33)
where
►A is the area of the smaller surface,
►e is a property of the surface called its emissivity,
►s is the Stefan-Boltzman constant.
► Q  es A[T 4  T 4 ]  0.8(5.67 x108 )(1) 10004  4004 
e
b
s


 44198.78W / m2
Million!
0.16 Million!
Black surface>1 m2 but only the part that “sees” the 1 m2 matters.
Convection
►Convection is energy transfer between a solid
surface and an adjacent gas or liquid by
conduction!
►The bulk flow within the gas or liquid
dT
determines the dx
►The rate of energy transfer by convection is
quantified by Newton’s law of cooling.
Convection
►Transistors use electrical
energy transferred to them by
the power supply as work and
dissipate that energy as heat!
A is the area of the transistor’s surface
►Energy is transferred in the direction of the arrow and
quantified by
Qc   cooling air A
dT
dx
 hA[Tb  Tf ]
Eq. 2.34
surface
►h is a parameter called the convection heat transfer
coefficient defined as: kcooling air dT
h
dx x0
(Tb  T f )
►Units of h are W/m2-K, units of k are W/m-K
Mechanical Energy Transfer by Work
►Energy can be transferred to and from a
system by mechanical work.
►You have studied work in mechanics and
those concepts are retained in the study of
thermodynamics.
►However, thermodynamics requires a
broader interpretation of work to allow
exchanges with other forms of energy.
Illustrations of Work
►When a spring is compressed,
energy is transferred to the spring by
work.
►When a gas in a closed vessel is
stirred, energy is transferred to the
gas by work.
►When a battery is charged
electrically, energy is transferred to
the working medium by work.
►Internal combustion engines drive piston and turn
flywheels to generate work.
►Gas turbines convert chemical energy into
mechanical energy and then into work.
Sign Conventions and Units of Work & Power
►The symbol W denotes an amount of energy transferred by
work.
Ft-lbm-ft/(s2); m-kg-m/(s2) = m-N which lead to
ft-lbf and Btu; Joules, kJ, MJ
►Since engineering thermodynamics is often concerned with
engines whose purpose is to deliver work, it is convenient to
regard the work done by a system as positive.
►W > 0: work done by the system
►W < 0: work done on the system
The same sign convention is used for the rate of energy W
transfer by work – called power- units are Btu/hr in British,
Watt, kW, MW in SI and Horsepower  in both.
Mechanical Work Example
• An object of mass 80 lb (or
36.29 kg), initially at rest,
experiences a constant
horizontal acceleration of 12
ft/s2 (or 3.6576 m/s2) due to the
action of a resultant force that is
applied for 6.5 s. Determine the
work of the resultant force, in
ft-lbf, in Btu, in J and kJ.
• Given
–
–
–
–
m = 80 lb or 36.29 kg
V1 = 0 ft/s or 0 m/s
a = 12 ft/s2 or 3.6576 m/s2
t = 6.5 s
• Find
– W in ft-lbf and Btu?
– And W in J and kJ
• Sketch
R
m
• Assumptions
z
– The 80 lb (36.29 kg) mass is
the system.
– Motion is horizontal, so the
system experiences no
change in potential energy.
– The horizontal acceleration
is constant.
x
• Basic Equations
W 
a
dV
dt

1
m V22  V12
2
dV  adt

V2  V1  a t 2  t1 


13
Mechanical Work Example
• Solution
R
m
z
x
SI System
V2  0  3.6576m / s 2 6.5s  0
V2  23.77 m s
V2  V1  a t 2  t1 

 0
W

1
m V22  V12
2

British System
V2  0  12 ft s 2 6.5s  0
V2  78 ft s
1
1lbf
2
 7560 ft  lbf
80lb  78 ft s 
2
32.2lb  ft s 2
1Btu
W  7560 ft  lbf
 9.71Btu
778lbf  ft
W
(1) Work does not depend on the units we use to measure it! Different
numerical values are assigned to identical work in different measuring
systems!
(2) See Conversion factors on inside cover of book.
10.255 kJ = 9.71 Btu because 1Btu=1.0551 kJ or 1 kJ = 0.9478 Btu 14
Sign Convention
• Our sign convention for work is easy to
remember:
– Work done by a system is considered to be
useful to mankind, so is defined to be positive.
– Therefore work done by the accelerator on the
particle is positive.
– Of course, if the work for “the system” defined
as “the particle” is to be calculated, then it is
negative but equal in magnitude to the work
done by the accelerator.
15
Piston Cylinder Systems
• Piston cylinder systems are widely used
• There function is to transfer expansion and
compression energy change into linear
motion and eventually rotary motion.
Applications: I. C. engines, hydraulic jacks,
bicycle air-pump, balloon inflator etc.
Stroke=Crank circle diameter. The cylinder
length must clear the end to end motion of
the connecting rod. The clearance volume defines
the compression ratio. The BDC volume defines the
cylinder capacity. The pressure, temperature and volume
within the cylinder are related and determine power output.
Expansion and Compression Work
W  Fdx
F  PA Adx  dV
W  PdV
The above derivation is applicable to
experimental pressure volume traces (see Fig. 2.5 in text)
as well as theoretical approximations to
processes for defining the system behavior.
Work is a path function and can not be evaluated by just knowing the end states 1 and 2.
Also, in writing the above equations, the assumption that the pressure in the cylinder is
uniform through out the volume has been made. This makes the work a quasi-steady
approximation to reality. None the less, this approximation has been found to be very
useful in industry.
Expansion and Compression Work
W  Fgasdx  PgasA p dx
2
1W2   PgasdV
1
If gas volume decreases, work is negative and is done on the gas.
If gas volume increases, work is done by the gas on the piston and
hence on the connecting rod and the crank shaft etc.
Practice these derivations
2
P  Const.1W2  Pgas  dV  Pgas(V2  V1)
1
2 PV
V
PV  Const.1W2   ( 1 1 )dV  P1V1 ln 2
V
V1
1
2 PV n
P V  PV
n
PV  Const.1W2   ( 1 1 )dV  2 2 1 1
n
1 n
1 V
Examples of work functions involving
different processes: Shaft Work
W  ss2 F  d s
1
W  Fds
Fds d
W  d
W  Dt
W  
τ – torque
ω – angular velocity (rad/s)
19
Examples of work functions involving different
processes: Spring Work
W  ss2 F  d s
1
Wspring  Fdx
F  kx

1
Wspring  k x22  x12
2

k – spring constant
xi – displacement from equilibrium
20
Examples of work functions involving different
processes: Work done by “flowing” electrons
Electric Power
W  e i
i –
eR ––
electric current (amp)
potential difference (V)
resistance (ohms)
Ohm’s Law
e  Ri
21
Additional examples of work
1. Torsion of a solid bar
See eq. 2.18
2. Stretching of a liquid film
See eq. 2.19
3. Charging of Electrolytic cell, Electric Field, Magnetic Field
Work done by electromotive force
Work done by dielectric in a uniform electric field
Work done by magnetic material in a field
Summary
►Kinetic Energy and Potential Energy are macroscale mechanical energies of a mass.
►Internal Energy is an extensive property of a working
substance and is defined by composition,
temperature, and pressure.
►Internal Energy changes by heat transfer and work
interactions.
►Heat Transfer is a result of temperature difference
and is by conduction, convection and
radiation.
Summary
►We defined gravitational potential energy and
change in this quantity and its relation to the
distance of an object from the earth’s center or
surface.
►We defined kinetic energy using the concept of force
times the displacement being equal to the work
done.
► We introduced the Conservation of Mechanical
Energy principle involving a balance between
the kinetic energy and the potential energy
exchange and defined Mechanical Work and the
sign convention associated with it.
Summary
►We defined expansion and contraction work and
calculated work associated with a process in a
piston cylinder device.
►We learned the potential for extension of our
mechanical work knowledge metaphorically to
electrical, magnetic, surface tension, torsion and
other work interactions.
►We learned about calculation of “Pdv” work for
experimental P-v diagrams as well as idealized
P-v compression and expansion processes.
Understand the positive and negative work
sign convention intuitively.