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Prof. Siyoung Jeong
Thermodynamics I
MEE2022-02
Spring 2014
Fundamentals of Thermodynamics
Chapter 3
First Law of Thermodynamics and
Energy Equation
Thermal Engineering Lab. 2
3.1 The energy equation
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 3
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 4
Chapter 3. First law of thermodynamics and energy equation
PEKEUE
EnergyPotentialEnergyKineticEnergyInternalE
mgzPEmVKE ,2
1 2
2 2
2 12 1 2 1 2 1
2
2 2
2 12 1 2 1 1 2 1 2
( )( )
2
2
( )( )
2
dE dU m d mgdz
m V VE E U U mg z z
mVdU d d mgz Q W
m V VU U mg z z Q W
V V
Thermal Engineering Lab. 5
Ex. 3.1 A tank containing a fluid is stirred by a paddle wheel. The work input to
the paddle wheel is 5090 kJ. The heat transfer from the tank is 1500 kJ.
Consider the tank and the fluid inside a control surface and determine the
change in internal energy of this control mass.
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 6
3.2 The first law of thermodynamics
Chapter 3. First law of thermodynamics and energy equation
• For a control mass undergoing a cycle
WQ
WQJ
Thermal Engineering Lab. 7
Chapter 3. First law of thermodynamics and energy equation
• For a change in state of a control mass
WQ
121 BA
1
2
2
1
1
2
2
1BABA WWQQ
1 2 1C B
2 1 2 1
1 2 1 2C B C BQ Q W W
Thermal Engineering Lab. 8
Chapter 3. First law of thermodynamics and energy equation
1 1 1 1
2 2 2 2
1 1
2 2
A C A C
A A C C
Q Q W W
Q W Q W
Q W
depends only on the initial and final state not on the path.
122121 EEWQ
dEWQ
Thermal Engineering Lab. 9
3.3 The definition of work
Chapter 3. First law of thermodynamics and energy equation
2
1
2
121 xdFdxFW
W = +: done by a system
W = - : done on a system부호
[ / sec] [ ]
J N m
WW J W
dt
Thermal Engineering Lab. 10
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 11
Chapter 3. First law of thermodynamics and energy equation
2 2 2
1 21 1 1
W F dx Frd Td
W F dx Frd Td
W dx dW F F V Fr T
dt dt dt
Ww
m
Thermal Engineering Lab. 12
Ex. 3.2 A car of mass 1100 kg drives with a velocity such that it has a kinetic
energy of 400 kJ (see Fig. 3.6). Find the velocity. If the car is raised with
a crane, how high should it be lifted in the standard gravitational field to
have a potential energy that equals the kinetic energy?
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 13
Ex. 3.3 Consider a stone having a mass of 10 kg and a bucket containing 100 kg
of liquid water. Initially the stone is 10.2 m above the water, and the
stone and the water are at the same temperature, state 1. The stone then
falls into the water.
Determine ΔU, ΔKE, ΔPE, Q and W for the following changes of state,
assuming standard gravitational acceleration of 9.80665 m/s2.
Chapter 3. First law of thermodynamics and energy equation
a. The stone is about to enter the water, state 2.
b. The stone has just come to rest in the bucket, state 3.
c. Heat has been transferred to the surroundings in such an amount that
the stone and water are at the same temperature, T1, state 4.
Thermal Engineering Lab. 14
3.4 Work done at the moving boundary of a simple compressible system
Chapter 3. First law of thermodynamics and energy equation
2
1
2
1
2
121 PdVPAdxdxFW
PAF
::
::
WdV
WdV
Thermal Engineering Lab. 15
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 16
Ex. 3.4 Consider a slightly different piston/cylinder arrangement, as shown in
Fig. 3.10. In this example, the piston is loaded with a mass mp, the
outside atmosphere P0, a linear spring, and a single point force F1. The
piston traps the gas inside with a pressure P.
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 17
Ex. 3.5 Consider the system shown in Fig. 3.12, in which the piston of mass mp
is initially held in place by a pin. The gas inside the cylinder is initially at
pressure P1 and volume V1. When the pin is released, the external force
per unit area acting on the system (gas) boundary is comprised of two
parts :
Pext = Fext / A = P0 + mpg / A
Calculate the work done by the system when the piston has come to rest.
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 18
Chapter 3. First law of thermodynamics and energy equation
• Polytropic process work
2 2
1 21 1
2
1
2
1
21
1
1 1
2 1
1 11 12 1
1 1
1 1 1 2
1
1
1
( 1)
1
n
n
n
n n
nn n
n n
W W PdV
CdV
V
CV dV
VC
n
CV V
n
PVV V
n
PV V V
n
n
n
V
CP
CConstPV
.
n
VPVP
1
1122
Thermal Engineering Lab. 19
Chapter 3. First law of thermodynamics and energy equation
n
P
PVP
n
P
PVP
n
V
VVP
n
n
n
n
n
1
1
1
1
1
1
1
1
211
11
1
211
1
1
211
n
n
nn
P
P
V
V
P
P
P
P
V
V
VPVP
1
1
2
1
2
1
1
2
2
1
1
2
2211
Thermal Engineering Lab. 20
Chapter 3. First law of thermodynamics and energy equation
2
111
1
211
1
2
2
1
2
1
2
1
2211
ln
ln
ln
ln
.
P
PVP
V
VVP
V
VC
VC
dVV
CPdV
VPVPconstPV
Thermal Engineering Lab. 21
Ex. 3.6 Consider as a system the gas in the cylinder shown in Fig. 3.14; the
cylinder is fitted with a piston on which a number of small weights are
placed. The initial pressure is 200 kPa, and the initial volume of the gas
is 0.04 m3.
Chapter 3. First law of thermodynamics and energy equation
a. Let the Bunsen burner be placed under the cylinder, and let
the volume of the gas increase to 0.1 m3 while the pressure
remains constant. Calculate the work done by the system
during this process.
b. Consider the same system and initial conditions, but at the
same time that the Bunsen burner is under the cylinder and
the piston is rising. Remove weights from the piston at
such a rate that, during the process, the temperature of the
gas remains constant. Calculate the work.
Thermal Engineering Lab. 22
Ex. 3.6 (cont’d)
Chapter 3. First law of thermodynamics and energy equation
c. Consider the same system, but during the heat transfer
remove the weights at such a rate that the expression
PV1.3 = constant describes the relation between
pressure and volume during the process. Again, the
final volume is 0.1 m3. Calculate the work.
d. Consider the system and initial state given in the first
three examples, but let the piston be held by a pin so
that the volume remains constant. In addition, let heat
be transferred from the system until the pressure drops
to 100 kPa. Calculate the work.
Thermal Engineering Lab. 23
3.5 Definition of heat
Chapter 3. First law of thermodynamics and energy equation
Heat : Temp. difference에 의해 전달되는 에너지
Sign+: to a system
-: from a system
Thermal Engineering Lab. 24
3.6 Heat transfer modes
Chapter 3. First law of thermodynamics and energy equation
Conduction
Convection
Radiation
dx
dTkAQ
TAhQ
4
sATQ
Thermal Engineering Lab. 25
Ex. 3.7 Consider the constant transfer of energy from a warm room at 20℃ inside a
house to the colder ambient temperature of -10℃ through a single-pane
window, as shown in Fig. 3.16.
The temperature variation with distance from the outside glass surface is
shown by an outside convection heat transfer layer, but no such layer is
inside the room (as a simplification). The glass pane has a thickness of 5 mm
(0.005 m) with a conductivity of 1.4 W/m∙K and . The outside wind is
blowing, so the convective heat transfer coefficient is 100 W/m2 ∙K. With an
outer glass surface temperature of 12.1℃, we would like to know the rate of
heat transfer in the glass and the convective layer.
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 26
3.7 Internal energy – a thermodynamic property
Chapter 3. First law of thermodynamics and energy equation
:
:
um
U
U
Intensive property
fgf
gf
ggff
vapliq
xuu
xuuxu
umummu
UUU
)1(
Thermal Engineering Lab. 27
Ex. 3.8 Determine the missing property (P, T, or x) and v for water at each of the
following states:
Chapter 3. First law of thermodynamics and energy equation
a. T = 300℃, u = 2780 kJ/kg
b. P = 2000 kPa, u = 2000 kJ/kg
Thermal Engineering Lab. 28
3.8 Problem analysis and solution technique
Chapter 3. First law of thermodynamics and energy equation
Ex. 3.9 A vessel having a volume of 5 m3 contains 0.05 m3 of saturated liquid
water and 4.95 m3 of saturated water vapor at 0.1 MPa. Heat is transferred
until the vessel is filled with saturated vapor. Determine the heat transfer
for this process.
Thermal Engineering Lab. 29
Ex. 3.10 The piston/cylinder setup of Example 3.4 contains 0.5 kg of ammonia at -20 ℃with a quality of 25%. The ammonia is now heated to +20℃, at which state the
volume is observed to be 1.41 times larger. Find the final pressure, the work the
ammonia produced, and the heat transfer.
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 30
Ex. 3.11 The piston/cylinder setup shown in Fig. 3.20 contains 0.1 kg of water at 1000
kPa, 500 ℃. The water is now cooled with a constant force on the piston until it
reaches half of the initial volume. After this, it cools to 25℃ while the piston is
against the stops. Find the final water pressure and the work and heat transfer in
the overall process, and show the process in a P-v diagram.
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 31
3.9 The thermodynamic property enthalpy
Chapter 3. First law of thermodynamics and energy equation
경우인 0, KEPEconstP
1 2 2 1 1 2
1 2 2 1
1 2 2 1 2 2 1 1
2 2 2 1 1 1
( )
( ) ( )
Q U U W
W P V V
Q U U PV PV
U PV U PV
Pvuh
PVUH
fgf
gf
xhhh
xhhxh
)1(
Thermal Engineering Lab. 32
Ex. 3.12 A cylinder fitted with a piston has a volume of 0.1 m3 and contains 0.5 kg of
steam at 0.4 MPa. Heat is transferred to the steam until the temperature is
300 ℃, while the pressure remains constant. Determine the heat transfer and
the work for this process.
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 33
3.10 The constant-volume and constant-pressure specific heats
Chapter 3. First law of thermodynamics and energy equation
VdPdHQ
PdVdUWdUQ
PPP
P
vvv
v
T
h
T
H
mT
Q
mC
T
u
T
U
mT
Q
mC
11
11
CdTdudh
vdPduPvddudh
)(
Solid and Liquids
Thermal Engineering Lab. 34
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 35
3.11 The internal energy, enthalpy, and specific heat of ideal gas
Chapter 3. First law of thermodynamics and energy equation
dvv
udT
T
udu
vTuuGenerally
Tv
),(
Thermal Engineering Lab. 36
Chapter 3. First law of thermodynamics and energy equation
• Experiment of Gay-Lussac
12 2 1 12
2 1 2 2
1 1
2 1
( , ) ( )
( , ) ( ) 0
,
( , ) ( , )
0
g A B W
g A W
g A B g A
T
Q U U W
U U U T V V U T
U T V U T
T T
U T V V U T V
u
v
실험 결과
dTmCdU
dTCdTT
udu
v
v
v
0
Thermal Engineering Lab. 37
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 38
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 39
Chapter 3. First law of thermodynamics and energy equation
)(
)(
Tfh
RTTu
Pvuh
dTCdh
T
hC
P
P
P
0
RCC
RCC
RdTdTCC
RdTdudh
RTupvuh
vP
vP
vP
00
00
00 )(
Thermal Engineering Lab. 40
Ex. 3.13 Calculate the change of enthalpy as 1 kg of oxygen is heated from 300 to
1500 K. Assume ideal gas behavior.
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 41
Ex. 3.14 A cylinder fitted with a piston has an initial volume of 0.1 m3 and contains
nitrogen at 150 kPa, 25 ℃. The piston is moved, compressing the nitrogen
until the pressure is 1 MPa. and the temperature is 150℃. During this
compression process heat is transferred from the nitrogen, and the work done
on the nitrogen is 20 kJ. Determine the amount of this heat transfer.
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 42
Ex. 3.15 A 25 kg cast-iron wood-burning stove, shown in Fig. 3.27, contains 5 kg of
soft pine wood and 1 kg of air. All the masses are at room temperature, 20 ℃,
and pressure, 101 kPa. The wood now burns and heats all the mass uniformly,
releasing 1500 W. Neglect any air flow and changes in mass and heat losses.
Find the rate of change of the temperature (dT/dt) and estimate the time it will
take to reach a temperature of 75℃.
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 43
3.12 General system that involve work
Chapter 3. First law of thermodynamics and energy equation
1. Wire
2. Surface Tension dAW S
AEe
dLW
T
Thermal Engineering Lab. 44
Ex. 3.16 During the charging of a storage battery, the current i is 20 A and the voltage
ε is 12.8 V. The rate of heat transfer from the battery is 10 W. At what rate is
the internal energy increasing?
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 45
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 46
3.13 Conservation of mass
Chapter 3. First law of thermodynamics and energy equation
2mcE
),( energyElightofvelocityc
Thermal Engineering Lab. 47
Ex. 3.17 Consider 1 kg of water on a table at room conditions 20 ℃, 100 kPa. We want
to examine the energy changes for each of three processes: accelerate it from
rest to 10 m/s, raise it 10 m, and heat it 10℃.
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 48
3.14 Engineering applications
Chapter 3. First law of thermodynamics and energy equation
Thermal Engineering Lab. 49
Chapter 3. First law of thermodynamics and energy equation