Transcript **** 1

1
15
In the mid-1800s, Mayer, Helmholtz, and Joule discovered independently
that heat is simply a form of energy.
JQ  K
dT
dx
1853: Wiedemann and Franz law (good electrical conductors are generally good
thermal conductors)
The ratio between heat conductivity and electrical conductivity (divided by
the temperature) is essentially constant for all metals
The thermal conductivity only varies within four orders of magnitude while
the electrical property varies about 25 orders of magnitude. (Fig. 18.1)
2
Heat in physics is defined as energy transferred by thermal interactions. Heat flows
spontaneously from systems of higher temperature to systems of lower temperature.
When two systems come into thermal contact, they exchange energy through the
microscopic interactions of their particles. When the systems are at different
temperatures, this entails spontaneous net flow of energy from the hotter to the
cooler, so that the hotter decreases in temperature and the cooler increases in
temperature. This will continue until their temperatures are equal. Then the net flow
of energy has settled to zero, and the systems are said to be in a relation of thermal
equilibrium. Spontaneous heat transfer is an irreversible process.
The first law of thermodynamics states that the internal energy of an isolated system
is conserved. To change the internal energy of a system, energy must be transferred
to or from the system. For a closed system, heat and work are the mechanisms by
which energy can be transferred. For an open system, internal energy can be
changed also by transfer of matter.[6] Work performed by a body is, by definition, an
energy transfer from the body that is due to a change to external or mechanical
parameters of the body, such as the volume, magnetization, and location of center of
mass in a gravitational field.[2][7][8][9][10][11]
When a body is heated, its internal energy increases. This additional energy is stored
as kinetic and potential energy of the atoms and molecules in the body. [12] Heat
itself is not stored within a body. Like work, it exists only as energy in transit from
one body to another or between a body and its surroundings.
(from wikipedia)
15.1. Heat, Work, And Energy
First law of thermodynamics
E  W  Q
E : internal energy change of the system
W : the work on the system
Q : the heat received by the system
In this chapter, We limit our consideration to processes for which W
can be considered to be Zero.
E  Q
Energy, work, and heat have same unit.
1 cal = 4.184 J
1 J = 0.239 cal
4
15.2. Heat Capacity c'
Heat capacity : the amount of heat which needs to be transferred to a
substance in order to raise its temperature by a certain
temperature interval.
Generally, it is interested in two kinds : at constant volume & at
constant pressure
 E 

Cv  
 at constant V

T

v
 H 
Cp  
 at constant P
 T  p
Enthalpy is a measure of the total energy of a
thermodynamic system. It includes the internal energy,
which is the energy required to create a system, and the
amount of energy required to make room for it by
displacing its environment and establishing its volume
and pressure.
H=E+PV
These relationship is….
Cv  Cp 
5
 TV

2
1 V
( )P
V T
1 V
 = isothermal compressibility   ( )T
V P
T = temperature
V = volume
 = volumetric thermal expansion 
 2TV
Proving Cv  Cp 

U
U
)T dV  (
)V dT
V
T
U
U
dU  (
)V dS  (
) S dV
S
V
dU  (
 H   U   U   ( PV )   U 
Cp  Cv  
 
 
 
 

 T P  T V  T P  T P  T V
 U   U   V   U 
 U   U 

 
 
 
  V 
 

 T P  V T  T P  T V
 V T  T V
and
 U   U   S   U 
 S 
 P 

 
 
 
 T 
 P T 
 P
 V T  S V  V T  V S
 V T
 T V
 U  T
 
P
 
 V T 
6
 V 


T P 
 P 



 

 T V  V 


 P T
 2TV
 U 
 U   U 
 T
  U 
 U 


V



V


P


  PV  



 


 



 T P
 V T  T V
 
  T V
 T V
 2TV
 2TV
 U 
 U 
Cp  C v 
  PV  
   PV  
 


T

T


V

V
 2TV
 C v  Cp 

 ( PV ) 
 (V ) 

  P
   PV
 T P
 T P
15.3. Specific Heat Capacity, c
Specific heat capacity is the heat capacity per unit mass
c
C
m
(
J
)
gK
E
 E 
 C  cm  
 
 T  v T
E  Q  mTc
'
v
15.4. Molar Heat Capacity, cv
Molar heat capacity is the heat capacity per mole
C
c
n
N
n
N0
E
E
 C  cv  M  ( )v 
T
T
'
v
7
(
J
)
mol  K
8
298K
At room temperature, molar heat capacity
at constant volume is approximately 25 J/mol·K
for most solids. (discovered by Dulong and
Petit)
Exception : carbon only reach
25J/mol·K at high temperature
9
All heat capacities are zero at T = 0K.
Near T= 0K, heat capacities are climb in proportion to T3
Debye Temperature θD: a temperature at which heat capacities reach
96% of their final value.
10
15.5. Thermal Conductivity, K
Heat flux is proportional to the temperature gradient.
The proportionality constant is called thermal conductivity .
JQ  K
dT
dx
J Q  heat flux (unit:
unit of K ( J/m  s  K ) dT
Joule
)
2
m s
 temperature gradient (unit:
dx
K (or  )  thermal conductivity
Negative sign indicates that the heat flows from the hot to the cold
end.
11
K
)
m
12
15.6. The Ideal Gas Equation
In ideal gas,
PV  nRT
P
V
n
R
T
pressure of the gas
volume of the gas
the amount of substance
universal gas constant
the thermodynamics temperature
R  kB N0  8.314(J/mol  K)  1.986(cal/mol  K)
k B  Boltzmann constant
N 0  Avogadro constant
This equation is a combination of two experimentally obtained

thermodynamics.
PV = constant ( discovered by Boyle and Mariotte )
V T, at constant P ( discovered by Gay-Lussac )
13
15.7. Kinetic Energy of Gases
When a body is heated, its internal energy increases. This additional energy is stored as
kinetic and potential energy of the atoms and molecules in the body. [12] Heat itself is not
stored within a body. Like work, it exists only as energy in transit from one body to
another or between a body and its surroundings.
In Figure 19.2
dV  Adx  Avdt
v  velocity
The number of particles reaching the end face
z 
1
1
nv  dV  nv Avdt
6
6
nv  number of particles
The number of particles per unit time & unit area
that hit the end face
A
z
1
nv v
6
N
nv 
V
14
the number of particles per unit volume
The momentum change per unit time & unit area
1
1 N
p*  z  2mv   nv v  2mv    mv 2
6
3 V
This yields, for the pressure,
P
F ma d (mv) / dt dp / dt
1N



 p* 
mv 2
A
A
A
A
3V
PV 
Inserting
1
Nmv 2  nRT  nk B N 0T  k B NT
3
Ekin 
1 2
mv
2
,k B NT
 Ekin
15

1
1
2
N 2 mv 2  NEkin
3
2
3
3
 k BT
2
(kinetic energy of a particle)