Transcript Thermodynamics I Temperature

Thermodynamics I
Temperature
•
Thermal Equilibrium and Temperature. Temperature scales
•
Absolute Temperature Scale. The Ideal-Gas Law
•
The Kinetic Theory of Gases. Pressure and Temperature
Heat
•
Heat. Heat capacity and Specific Heat
•
Change of Phase and Latent Heat
•
Thermal expansion and Phase Diagrams
•
Heat Transfer
•
Transport Laws
References: Tipler; wikipedia, Britannica
Thermodynamics II
The First Law of Thermodynamics
•
Heat and Work. First Law of Thermodynamics
•
Heat and Work on Quasi-Static Processes for a Gas.
The Second Law of Thermodynamics
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Heat Engines and the Second Law of Thermodynamics
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Refrigerators and the Second Law of Thermodynamics
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The Carnot Engine
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Heat Pumps
•
Irreversibility and disorder. Entropy
References: Tipler; wikipedia,…
Temperature
Thermal Equilibrium and Temperature. Temperature scales
Our sense of touch can usually tell us if an object is
hot or cold. Usually we need get in touch –physical
contact- to appreciate if a body is hot or cold.
But our perception is very subjective.
Temperature:
measure of hotness
and coldness in
terms of any
arbitrary scales and
indicating the
direction which
energy
spontaneously flows
(from a hotter body
to a colder one)
A thermometer is any of class of instrument that measures the
temperature. Temperature is the physical magnitude that is
measured by thermometers.
A physical property that changes with the temperature is called
a thermometric property
- most solids an liquids expand when they are heated
- electrical resistance change when is heated
- in a gas pressure and volume change when it is heated
- radiation from the surface of a body depends on the
surface temperature
-……
References: Tipler; Britannica
Temperature
• Thermal Equilibrium and Temperature. Temperature scales
Thermal contact: Heat energy is transferred between
the bodies in thermal contact
Thermal equilibrium: When the thermometric
properties of the bodies in thermal contact do not change
If two objects are in thermal equilibrium with a
third, then they are in thermal equilibrium
each other
(Zeroth Law of thermodynamics)
Two objects are defined to have the same
temperature if they are in thermal equilibrium with
each other. Temperature may be defined as the
property of a system that determines whether it is
in thermal equilibrium with other system.
Temperature is one of the seven basic physical
quantities in term of which all other physical
quantities are defined. It is an “intensive” property,
as pressure or density. Length, mass are
“extensive”
Thermodynamics. Temperature
• Temperature scales
Calibration of a thermometer: Reproducibility
and Reliability.
When the thermometric property changes
lineally with the temperature, two fixed points
can be used to calibrate the thermometer.
Ice point temperature (normal
freezing point of water)
Steam-point temperature : normal
boiling point of water
Centigrade Temperature Scale
(Celsius scale)
Fahrenheit Temperature Scale
Absolute Temperature Scale
t F  95 t C  32
t C  95 ( t F  32)
T  tC  273.15
Derive and check the above expressions to convert Fahrenheit degrees temperature to
centigrade degrees temperature and the inverse relationship. The same to convert Kelvin
scale to centigrade. Apply to obtain the Fahrenheit normal human temperature if it is 36.5
Celsius degrees
Thermodynamics. Absolute Temperature Scale. Kelvin Scale.
A constant-volume gas
It is possible to define a temperature scale in a
independent way of the used thermometric substance
thermometer
Temperature of the boiling point of sulfur measured with
constant-volume gas thermometers . P100 is the pressure of the
gas at 100ºC
Plot of pressure versus
temperature for a gas,
as measured by a
constant-volume gas
thermometer. When
extrapolated to zero
pressure, the plot
intersects the
temperature axis at the
showed value of 273.25 ºC
The ideal-gas temperature scale
is defined so that the temperature
of the triple point state is 273.16
kelvins, K.
T
The triple point of water is the
unique temperature and pressure at
which water, water vapor and ice
coexist in equilibrium. [0.01 ºC and
4.58 mmHg]
Thermodynamics. Ideal Gas Law
The properties of gas samples that have low densities led to the
definition of the ideal-gas temperature scales. The behavior of
gases at this low densities was described
(1) by Boyle´s Law (1661)
PV = constant
(for a constant temperature)
(2) by Charles and Gay-Lussac Law (about 1800)
P = C1 T
(for a constant volume)
V = C2 T
(for a constant pressure)
T absolute temperatures; C1 and C2 constants
Ideal Gas-Law
PV  n R T
Equation of state of ideal gas
n = amount of gas expressed in moles
R : Universal gas constant
R = 8.314 J/(mol • K) =
= 0.082 atm • L/(mol • K)
The temperature of 0º (273.15 K) and
the pressure of 1 atm are often referred
as standard condition.
A mole (mol) of any substance is the
amount of substance that contains the
Avogadro number, NA, of atoms or
molecules, defined as the number of
carbon atoms in 12 g of 12C.
Thermodynamics. Dealing with the Ideal Gas Law
PV  n R T
Ideal Gas-Law
Equation of state of ideal gas
n = m/ M [mass of the substance in g/molecular mass] mol
R = 8.314 J/(mol • K) = 0.082 atm • L/(mol • K)
P

 RT
  R T
M
density
The mass per mole of a substance is called its
molar mass. (The terms molecular mass or
molecular weight are sometimes used
A gas has a volume of 2 L, a temperature of 30ºC, and a pressure of 1 atm. When the
gas is heated to 60ºC and compressed to a volume of 1.5 L, what is the new pressure
What is the density of dry air at standard conditions of pressure and temperature?. The
same at 20ºC; The same at 20ºC and 933 mb. Molecular mass of dry air: 28.97 g.
An automobile tire is filled to a gauge pressure of 200 kPa when its temperature is 20ºC.
After the car has been driven at high speeds, the tire temperature increases to 50ºC. (a)
Assuming that the tire volume does not change, find the gauge pressure in the tire (b)
Calculate the gauge pressure if the volume of the tire expands by 10%.
Thermodynamics. The Kinetic Theory of Gases.
Molecular Interpretation of Pressure and Temperature
Goal : To relate macroscopic point of view aboutt pressure
and temperature with the microscopic motion.
For a solid, these microscopic motions are principally the
vibrations of its atoms about their sites in the solid. For an
ideal monatomic gas, the microscopic motions are the
translational motions of the constituent gas particles. For a
multiatomic gas, vibrational and rotational motion should be
included too.
The kinetic theory of gases is able us to establish
quantitatively the relationship between pressure and
temperature with molecular motion for gases
The pressure that a gas exerts on its container is due to collisions between gas molecules and the
container walls. This pressure is a force per unit of area and, by Newton´s second law, this force is
the rate of change of momentum of the gas molecules colliding with the walls.
References
http://en.wikipedia.org/
wiki/Image:Translationa
l_motion.gif
Crystalline
Solids
The absolute
temperature is a
measure of the
average kinetic
energy of the
molecules.
Thermodynamics I
Temperature
•
Thermal Equilibrium and Temperature. Temperature scales
•
Absolute Temperature Scale. The Ideal-Gas Law
•
The Kinetic Theory of Gases. Pressure and Temperature
Heat
• Heat. Heat capacity and Specific Heat
• Change of Phase and Latent Heat
• Thermal expansion and Phase Diagrams
• Heat Transfer
• Transport Laws
References: Tipler; wikipedia, Britannica
Thermodynamics. Heat. Heat capacity and Specific Heat
Heat is the energy that is being transferred from one system to another as a
result of difference in temperature.
If two bodies at different temperature are brought together, energy is
transferred –i.e. heat flows- from the hotter body to the colder. The effect of
this transfer of energy usually, but non always*, is an increase in the
temperature of the colder body and an decrease of the hotter body; the
amount of heat that leaves one equals the amount that enters the other.
Heat Capacity and Specific Heat
Q  CT  m c T
C heat capacity; c specific heat
cC
m
Units of heat: Calorie [cal] : the amount of
energy to be transferred to raise the temperature
of one gram of water one centigrade degree.
1cal = 4.184 J
The amount of heat energy Q needed to
raise the temperature of a substance is
proportional to the temperature change
and to the mass of substance.
cwater: 1 cal/(g•ºC)= 1kcal/(kg•ºC)=
4.184 kJ/(kg•ºC) = 4.184 kJ/(kg•K)
The specific heat of a substance depends of the way as
the heat is transferred. The most commonly determined
specific heats are the specific heat at constant pressure
and the specific heat at constant volume
The heat capacity per mole is
called the molar specific heat
* The exceptions occurs during
a change of phase
Thermodynamics. Heat. Heat capacity and Specific Heat
Heat capacity: The amount of heat energy Q necessary to raise the
temperature of a substance by one degree.
The Heat capacity per unit mass is called specific heat
The Heat capacity per amount of substance (mol) is called the
molar specific heat
Specific Heat Molar Specific Heat
kJ/(kg•K)
kJ/(mol•K)
Water
4.184
75.3
Air
cP = 29.19 J/(mol•K); cV = 20.85 J/(mol•K). M=28.84 g
cP= 1.012 kJ/(kg•K); cV = 0.723 kJ/(kg•K);
Thermodynamics. Heat. Heat capacity and Specific Heat
Heat Capacity and Specific Heat
Q  CT  m c T
C heat capacity; c specific heat
cC
m
The amount of heat energy Q needed to
raise the temperature of a substance is
proportional to the temperature change
and to the mass of substance.
cwater: 1 cal/(g•ºC)= 1kcal/(kg•ºC)=
4.184 kJ/(kg•ºC) = 4.184 kJ/(kg•K)
How much heat is required to change 1.5 kg of ice at -20ºC and 1 atm into steam.
Typical volumetric heat capacity of a soil is 2.1 MJ/(m3 K). Estimate the absorbed
heat energy by a layer of 1 m of depth when its temperature is increased by10ºC.
Calculate the specific heat of the soil if the bulk density of the solid is 1.7 Mg/m3.
A great part of the soil are pores that can be filled by water. Then the volumetric
heat capacity of a soil will vary with its content of water. Explain the behavior
when the content of water increase.
Thermodynamics. Change of Phase and Latent Heat
Common types of phase change include fusion (liquid to solid), melting
(solid to liquid), vaporization (liquid to vapor or gas); condensation (gas
or vapor to liquid), and sublimation (solid directly to vapor).
When a phase change appears there is no temperature change when the
thermal energy is being transferred to the body in which the phase
change is occurring. In the case of a phase change the specific heat (or
capacity) is infinitum.
Latent Heat
Qf  m Lf
QV  m LV
Latent heat of fusion [or melting], Lf. At a pressure
of 1 atm, the latent heat of fusion for water is
Lf =333.5 KJ/kg
Latent heat of vaporization, LV . For water at a
pressure of 1 atm, the latent heat of vaporization is Lf
= 2.25 MJ/kg (at boiling point).
3
Latent heat of vaporization of water depends 

2
.
501

(
2
.
361
x
10
)t
on the temperature. water
1

latent
heat
of
vaporizati
on
[
MJkg
]
Latent heat of water at 20ºC is 2.45 MJ/kg.
A common relationship is: t temperature [º C ]
Thermodynamics. Change of Phase and Latent Heat
Common types of phase change include fusion, freezing, (liquid to
solid), melting (solid to liquid), vaporization (liquid to vapor or gas);
condensation (gas or vapor to liquid), and sublimation (solid directly to
vapor and vapor to solid –in some places the last process is called
deposition-).
When a phase change appears there is no temperature change when the
thermal energy is being transferred to the body in which the phase
change is occurring. In the case of a phase change, the specific heat (or
capacity) is infinitum.
http://www.usatoday.com/weather/wwatphse.htm
Thermodynamics. Change of Phase and Latent Heat. Water
http://hyperphysics.phyastr.gsu.edu/hbase/thermo/phase.html
Thermodynamics. Evaporation
Evaporation
Ordinary evaporation is a surface phenomenon - some molecules have
enough kinetic energy to escape. If the container is closed, an equilibrium is
reached where an equal number of molecules return to the surface. The pressure
of this equilibrium is called the saturation vapor pressure.
In order to evaporate, a mass of water must collect the large heat of vaporization,
so evaporation is a potent cooling mechanism. Evaporation heat loss is a major
climatic factor and is crucial in the cooling of the human body.
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html
Thermodynamics. Evaporation vs. Boiling
Evaporation vs Boiling
Ordinary evaporation is a surface phenomenon - since the vapor
pressure is low and since the pressure inside the liquid is equal to
atmospheric pressure plus the liquid pressure, bubbles of water
vapor cannot form. But at the boiling point, the saturated vapor
pressure is equal to atmospheric pressure, bubbles form, and the
vaporization becomes a volume phenomena.
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html
Thermodynamics. Thermal expansion
Thermal expansion. When the
temperature of an object increase, the
object usually increase
L
  T
L
dV
  T
V
 : coefficient of linear exp ansion
 : coefficient of volume exp ansion
Do holes
expand?
Thermodynamics. Thermal Expansion. Case of Water
Volume of 1 g of water at atmospheric pressure versus temperature. The minimum
volume, which corresponds to the maximum density, occurs at 4ºC. [ Supercooled water is
water that is cooled below the normal freezing point without solidifying. It is showed in the
figure]
Discuss the expansion of water in the case of freezing (or fusion) liquid to solid (ice)-. See the density of ice and the density of liquid
water
Thermodynamics. Phase Diagramas. Case of Water
The diagram P-T for water at a constant volume. The pressure and
temperature scales are not linear.
Thermodynamics. Heat Transfer
Heat Transfer
The spontaneous transfer of heat energy is from a high temperature object to a
lower temperature object. Heat Transfer focus on the energy rate that is being
transferred and on the mechanism of transport.
Thermal energy is transferred from one place to another by three types of
processes. The driving force of heat transfer flow is always the difference of
temperature:
• Conduction, In this case, the mechanism of heat energy transport is the
interactions among atoms or molecules (collisions), although there is no mass
motion. It is the case of heat transfer in opaque solids
• Convection, heat energy is transported by direct mass transport. Convective
currents are in charge of the transport
• Radiation; heat energy is transferred through space in the form of
electromagnetic waves [ or photons] that move at light speed. Sun´s energy
In all cases we can write:
rate of net heat transfer = difference of temperatures/ resistance