Download Thermodynamics study the thermal energy (often called the internal

Chapter 13 temperature, heat transfer, and
first law of thermodynamics
Thermodynamics study
the thermal energy (often
called the internal energy)
of systems.
The central concept of
thermodynamics is
temperature.
Temperature is one of the
seven SI base quantities.
What is temperature?
Sense of hot and cold is not
always reliable.
1
§13.1 Some important concepts
1. The simple thermodynamic system
A thermodynamic system is defined as a
collection of many particles such as atoms
and/or molecules.
A simple thermodynamic system is a system
that is macroscopic, homogeneous, isotropic,
uncharged, chemically inert, and experiences
no change in its total mechanical energy. The
system is sufficiently large that surface effects
can be neglect. No electric or magnetic fields
are present, and gravitational fields are
irrelevant.
§13.1 Some important concepts
2. Thermal equilibrium
Put two system in thermal contact, after long
enough time, if their properties (for instance:
the temperature) do not change, they are in
thermal equilibrium.
3. The zeroth law of thermodynamics
2
§13.1 Some important concepts
If body A and B are each in thermal equilibrium
with a third body T, then they are in thermal
equilibrium with each other.
Every body has a property called temperature.
When two bodies are in thermal equilibrium,
we say that they have same temperature. And
vice versa.
4. Temperature
There exists a scalar quantity called
temperature, which is a property of all
thermodynamics systems in equilibrium. Two
systems are in thermal equilibrium if and only
if their temperatures are equal.
§13.1 Some important concepts
Measuring temperature:
1types of thermometer
By using some physical properties of matter—
thermometric property that change with
temperature.
Volume of mercury—common
household and laboratory
thermometers.
Constant volume gas
thermometer: as shown in
Figure
3
§13.1 Some important concepts
Platinum resistance thermometers—electrical
resistance as a thermometric property
Thermocouple—different thermal properties of
two kind of metal
§13.1 Some important concepts
2Calibrating thermometers
100( X − X 0 )
100(Y − Y0 )
t (Y ) =
X 100 − X 0
Y100 − Y0
o
t ( X 0 ) = t (Y0 ) = 0 C t ( X 100 ) = t (Y100 ) = 100o C
t( X ) =
4
§13.1 Some important concepts
3 Ideal gas temperature scale (Kelvin scale)
How to avoid the dependence of the particular
means or substance?
The triple point of water: t=0.01ºC, T=0K
R. Boyle: PV = cons tan t
L. J. Gay-Lussac: V = V0 (1 + α V t )
J. A. C. Charles: P = P0 (1 + α P t )
When P0Æ0
α V = α P = α = 1 / T0
T0 = 273.15o C
§13.1 Some important concepts
Experiments: P0 ∝ m P = P0 (1 + α P t )
The intercept of the line on the axis t is 1 / α P .
For all kind of gas, when m is decrease, P0Æ0.
α V = α P = α = 1 / T0
T0 = 273.15o C
P
Gas 1
Gas 2
P0
Gas 3
t / Co
− T0
0
100
5
§13.1 Some important concepts
T=0K is called absolute zero.
One Kelvin is defined to be 1/273.16 of the
temperature of the triple point of water.
Ideal gas temperature scale:
P
)
gas → 0 P
3
T = 273.16K ( lim
T = t celsius + 273.15 (K)
§13.2 Heat transfer, and calorimetry
1. Heat and heat transfer
Heat is energy that flow between a system
and its environment simply because of the
difference of temperature between them.
Characteristic:
1the process of heat transfer continues until
the both systems reach to thermal equilibrium
(have same temperature);
2heat transfer occurs from the hotter system
to the cooler system;
3heat transfer is essentially a microscopic
atom-to-atom transfer of energy, it is distinctly
different from macroscopic wok.
6
§13.2 Heat transfer, and calorimetry
Q < 0, heat transfer from a system;
Q > 0, heat transfer to a system.
2. Temperature change and specific heat
dQ
Experiment:
dQ = cmdT
dT ∝
m
c=
1 dQ
--specific heat [J/kg·K]
m dT
§13.2 Heat transfer, and calorimetry
dQ = cmdT = ncmolar dT
cmolar =
1 dQ
--molar specific heat[J/mol·K]
n dT
Molar specific heat is the heat transfer to one
mole of the material needed to raise it
temperature by one Kelvin.
1 dQ
1 dQ
cP = (
)P
For gases: cV = ( )V
m dT
m dT
cmolar V =
1 dQ
(
)V
n dT
cmolar P =
1 dQ
(
)P
n dT
7
§13.2 Heat transfer, and calorimetry
Notice:
1the specific heat of a substance usually
varies with the temperature;
2in this text , we consider the specific heat to
be independent of temperature.
3. Changes of phase and latent heat
Latent heat—the heat transfer needed to
change the phase of a substance.
1first-order phase transitions
The phase transitions involved latent heats
are called first-order phase transitions. For
instance: converting water at 100ºC to
steam at 100ºC.
§13.2 Heat transfer, and calorimetry
2second-order phase transitions
The phase transitions that have zero latent
heats are called second-order phase
transitions.
3latent heat (heat of fusion and heat of
vaporization)
Q = mL or Q = nLmolar
Example: P605 13.12
8
§13.3 mechanisms of heat transfer
1. reservoirs
Reservoir is a special thermodynamics system.
When a system in thermal
contact with a reservoir
experiences heat transfer to
or from the system until it
has the same temperature as
the reservoir. The
temperature of the reservoir
does not change.
Q
Q Q = cm∆T ∴ ∆T =
cm
if cm >> Q then ∆T → 0
§13.3 mechanisms of heat transfer
2. Mechanisms of heat transfer
1conduction
Heat transfer by conduction depends on
critically on the material bridging or
connecting the warmer and cooler regions.
dQ
dT
Heat flow:
= − kA
dt
dx
k—thermal conductivity
A—the the area of thermal contact
dT
dx
--Temperature gradient
9
§13.3 mechanisms of heat transfer
For a steady state:
∫
T
x
TH
s=
d T = ∫ − sd x
dT
= − s = constant
dx
d
0
TH − T TH − TC
=
x
d
dQ
T − TC
T − TC
= kA H
=A H
dt
d
R
R=
d
--thermal resistance
k
§13.3 mechanisms of heat transfer
For material in series:
dQ
T − TC
T − TC
=A H
=A H
dt
R1 + R2
Rtotal
Rtotal = R1 + R2 + L + RN
d 2 d1
10
§13.3 mechanisms of heat transfer
For material in parallel:
dQ
dQ
dQ
(
)total = (
)1 + (
)2
dt
dt
dt
T − TC
T − TC
= A1 H
+ A2 H
R1
R2
A A
= (TH − TC )( 1 + 2 )
R1 R2
2convection(omit)
3radiation
dQ
= −eAσT 4
dt
dQ
= aAσT 4
dt
--Radiation
---absorb
§13.4 energy conservation: the first law of
thermodynamics and the CWE theorem
1. Thermodynamics process
A thermodynamics process is any way that
a system changes from one state of thermal
equilibrium to another such state.
2. Quasi-static(reversible) processes
If a thermodynamics system undergoes a
change from one state of thermal
equilibrium to another slowly enough so at
any instant the entire system essentially is
in thermal equilibrium, then we say the
process is quasi-static process.
11
§13.4 energy conservation: the first law of
thermodynamics and the CWE theorem
3. Irreversible processes
Any process that is not quasi-static process
and reversible is called irreversible.
In nature, all thermodynamic processes really
are irreversible.
4. Energy
1macroscopic energy E = KE + PE
2microscopic energy—internal energy U
E—ordered energy
U—disordered energy
∆E and ∆U is significant.
§13.4 energy conservation: the first law of
thermodynamics and the CWE theorem
3The mechanisms of energy transfer
Heat transfer to a system (conduction,
convection, radiation), instigated by
temperature differences:
Microscopic mechanism
Notice: Q is not a state variable, the internal
energy U is a state variable.
Work done on the system, instigated by
macroscopic forces:
Macroscopic mechanism
12
§13.4 energy conservation: the first law of
thermodynamics and the CWE theorem
5. Fundamental energy conservation law
Q + W ′ = ∆U + ∆E
Q—heat transfer
W ´--work done on the system by external
macroscopic, nonconservative forces
∆E= ∆ KE+∆PE—change in mechanical energy
of the system
∆U—change in the internal energy
Pure classical mechanics:
Q = 0 ∆U = 0
W ′ = ∆KE + ∆PE = ∆E
§13.4 energy conservation: the first law of
thermodynamics and the CWE theorem
Pure thermodynamics (simple system):
∆E = 0 Q + W ′ = ∆U
W ′ = −W
First law of thermodynamics:
Q = ∆U + W
W—work done by the system on the surroundings
Notice:
1It is a statement of conservation of energy
for pure thermodynamic system;
13
§13.4 energy conservation: the first law of
thermodynamics and the CWE theorem
Notice:
2∆E=0, there is no changes in sum of the
macroscopic kinetic and potential energy of
the system;
3Q>0, heat transfer to the system, W>0, the
work done by the system on its surrounding
environment;
4both the heat transfer to the system and the
work done by the system depend on the
particular way the system interacts with its
environment.
§13.4 energy conservation: the first law of
thermodynamics and the CWE theorem
6. The connection between the CWE theorem and
the general statement of energy conservation
For an inelastic collision of two particles:
r
mviˆ = ( M + m )v ′
M
m
r
v
r
m
v′ =
viˆ
M +m
1
1
∆E = ( M + m )v ′ 2 − mv 2
2
2
1
M
=− (
)mv 2
2 M +m
CWE theorem:
W ′ = ∆E
14
§13.4 energy conservation: the first law of
thermodynamics and the CWE theorem
but W ′ = WG′ + W N′ = 0 ∆E ≠ 0
Use the general statement of energy conservation
Q + W ′ = ∆U + ∆E
Q = 0 W′= 0
∆U = − ∆E = − ∆KE
∆U =
M
1
(
)mv 2
2 M +m
Conclusion: the missing kinetic energy
appears as an increase in the internal energy
of the system.
§13.5 work done by ideal gases in some
special processes
1. Ideal gas
Experiments show that: at low enough density,
all gases tend to obey the relation
PV = nRT = NkT
Gas constant
R = 8.32J/mol ⋅ K
Boltzmann constant k =
R
= 1.38 × 10 − 23 J/K
NA
2. Wok done by a system
r r
dW = F ⋅ dr
15
§13.5 work done by ideal gases in some
special processes
dW = PAiˆ ⋅ dxiˆ = PdV
x
Vf
W = ∫ PdV
Vi
dx
r
F
W>0
Vf
Vi
Work done by the system
§13.5 work done by ideal gases in some
special processes
Wnet
W<0
Vf
Vi
Work done on the
system
Work done by the
system in a cycle
process
16
§13.5 work done by ideal gases in some
special processes
Work is not state variable
§13.5 work done by ideal gases in some
special processes
3. Work done by ideal gas at special processes
1at constant volume
(isochoric process)
P
Vf
W = ∫ dW = ∫ PdV = 0
Vi
2at constant pressure
(isobaric process)
V
Vi
P
Vf
W = ∫ dW = ∫ PdV
Vi
= P (V f − Vi )
Vi
Vf
V
17
§13.5 work done by ideal gases in some
special processes
3at constant temperature (isothermal process)
W = ∫ dW = ∫
Vf
Vi
Pd V
P
nRT
dV
Vi
V
Vf
= nRT ln
Vi
=∫
Vf
Vi
Vf
V
4in thermal isolation (adiabatic
process)
γ
PV
γ
PiVi = PV γ
P = i γi
V
γ
γ
Vf
V f PV
PiVi
i i
W = ∫ PdV = ∫
dV =
(Vi1−γ − V f1−γ )
γ
Vi
Vi
γ −1
V
§13.5 work done by ideal gases in some
special processes
PiVi Vi γ −1
[( ) − 1]
γ −1 Vf
1
=
( PiVi − P f V f )
γ −1
W =
P
Vi
Vf
V
18