Lecture 4 First Law of Thermodynamics and Energy Equation (2)
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First Law of Thermodynamics and Energy Equation (2) (Lecture 4) 2021년 1학기 열역학 (M2794.001100.002) 송한호 (*) Some texts and figures are borrowed from Sonntag & Borgnakke unless noted otherwise.
Transcript of Lecture 4 First Law of Thermodynamics and Energy Equation (2)
First Law of Thermodynamics and Energy Equation (2)
(Lecture 4)
2021년 1학기열역학 (M2794.001100.002)
송한호(*) Some texts and figures are borrowed from Sonntag & Borgnakke unless noted otherwise.
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3.5 Definition of Heat
è Heat is defined as a form of energy that is transferred across the boundary of a system.
è Heat transfer is caused by temperature difference between two systems.
è A process with no heat transfer is called an adiabatic process.è Heat is an inexact differential as work:
dtQQ d
º! (J/kg) mQq ºò=
2
121 QQ d
First Law of Thermodynamics and Energy Equation
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3.6 Heat Transfer Modes
Conduction
Convection
Radiation 4s
dTQ kAdx
Q Ah TQ ATes
= -
= D
=
!
!
!
è Three major heat transfer modes:
(Source: www.beodom.com)
First Law of Thermodynamics and Energy Equation
è Internal energy (U) is an extensive property, or proportional to mass.
è Specific internal energy is an intensive property.
è Internal energy(u) is a thermodynamic property as T, P, v. Thus, it
can be used to determine the thermodynamic state.
è Internal energy is listed in thermodynamic tables.
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:
:
umUU
=
Extensive property
Intensive property
3.7 Internal Energy – A Thermodynamic Property
First Law of Thermodynamics and Energy Equation
è For thermodynamic tables of water in Sonntag’s textbook, saturated
liquid at triple point (0.01°C, 0.6113 kPa) is used as a reference
energy point, and the value of internal energy is taken as 0 (zero).
All other energy values are evaluated relative to this point.
è For saturated state, the similar approach (using quality, x) as for
specific volume is applied.
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fgf
gf
ggff
vapliq
xuuxuuxuumummu
UUU
+=
+-=
+=
+=
)1(
First Law of Thermodynamics and Energy Equation
3.9 The Thermodynamic Property – Enthalpy
è Consider a control mass undergoing a quasi-equilibrium constant-pressure process (assume no change in PE and KE).Then, the 1st law of thermodynamics is:
Here, define a new thermodynamic property, enthalpy, as:
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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 WW P V VQ U U PV PV
U PV U PV
= - += -
\ = - + -= + - +
PvuhPVUH
+=+= (extensive property)
(per unit mass)
First Law of Thermodynamics and Energy Equation
è Enthalpy is a point function and has an unit of energy (J).
è In many thermodynamic tables, enthalpy(h) is listed instead of internal energy(u). Then, internal energy can be evaluated from enthalpy as follows:
è For the enthalpy of a substance in saturation state, the enthalpy is given as:
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PvuhPVUH
+=+=
fgf
gf
xhhhxhhxh
+=
+-= )1(
Pvhu -=
First Law of Thermodynamics and Energy Equation
è Specific heat: the amount of heat required per unit mass to raise the temperature by one degree
è Consider two special cases:• Specific heat at constant volume
• Specific heat at constant pressure
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PdVdUWdUQ +=+= dd
PPPp T
hTH
mTQ
mC ÷
øö
¶¶
=÷øö
¶¶
=÷øö=
11dd
3.10 The Constant-Volume and Constant-Pressure Specific Heats
VdPdHVdPPVUdVdPPVddU
VdPVdPPdVdUQ
-=-+=-+=
-++=
)( )(
)(d
vvvv T
uTU
mTQ
mC ÷
øö
¶¶
=÷øö
¶¶
=÷øö=
11dd
TQ
mCTmCQ
dddd 1 =®=
First Law of Thermodynamics and Energy Equation
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è Specific heat is a thermodynamic property, independent of the particular process.
)( 100
12,
1221
TTmCUUkJQ
AVGv -=-==
)( 100
12,
1221
TTmCUUkJW
AVGv -=-==-
First Law of Thermodynamics and Energy Equation
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è Consider specific heats for solids and liquids. è The main difference between these states and gas state is
small specific volume and small change in specific volume as states change.
è Specific heats at const V and at const P are nearly the same!
(small change in volume, dv=0)
(small specific volume, v=0)
First Law of Thermodynamics and Energy Equation
è Internal energy(u), enthalpy(h), and specific heat(C) are thermodynamic properties, and thus, function of two other independent properties, e.g. (P,v), (P,T), (T,v) for a simple compressible pure substance.
è Strong dependence on temperature change, while weakdependence on pressure (or density) change.
è At high temperature and low pressure (or close to ideal gas), there is little pressure dependence.
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dvvudT
TuduvTuuGenerally
Tv÷øö
¶¶
+÷øö
¶¶
=®= ),(
3.11 The Internal Energy, Enthalpy, and Specific Heat of Ideal Gases
First Law of Thermodynamics and Energy Equation
è The internal energy of an ideal gas is a function only of temperature.
è Then, the enthalpy of an ideal gas is also a function only of temperature.
è Finally, the specific heats of an ideal gas is a function only of temperature.
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dvvudT
TuduvTuuGenerally
Tv÷øö
¶¶
+÷øö
¶¶
=®= ),(
dTduCdTCdT
TuduTfugasIdeal vv
v
=®=÷øö
¶¶
=®= 00 only )(
)( TfhRTuPvuh =®+=+=
00 dTdhCdTCdT
ThdP
PhdT
Thdh pp
PTP
=®=÷øö
¶¶
=÷øö
¶¶
+÷øö
¶¶
=
)( 0,0 TfCC pv =
=0
First Law of Thermodynamics and Energy Equation
è There is a relationship between specific heats at constant volume and constant pressure of an ideal gas:
è To evaluate the enthalpy of an ideal gas: è Constant specific heat:
è Varying specific heat w.r.t. temperature:
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(specific heats for some gases)
à or
ò=- 2
1012
T
T p dTChh
à
Where, (Table A.7 and A.8)
(Table A.6)
(Table A.5)
First Law of Thermodynamics and Energy Equation
