principles of refrigeration chapter 7
TRANSCRIPT
Gas Laws
Topics for Discussion
• Relationship Between Heat and Volume
• Relationship Between the Properties of Gases
Constant Temperature Processes
Constant Pressure Processes
Constant Volume Processes
Avogadro’s Law
The Ideal Gas Law
The Relationship Between
Heat and Volume
• Changes in the internal energy of a substance
produce corresponding changes in its volume.
• When a transfer of thermal energy increases
the internal energy of an uncontrolled
substance, two reactions typically occur.
• The thermal energy transfer increases the
temperature and volume of the substance.
The Relationship Between
Heat and Volume
• The rise in temperature is a consequence of the
increase in kinetic energy.
• The increased volume occurs in response to an
increase in potential energy that appears as an
increase in the distance between the
molecules.
• Conversely, when energy is transferred from a
substance, it contracts as temperature reduces.
The Relationship Between
Heat and Volume
• Tremendous pressures are created whenever a
substance in its solid or liquid phase is
restrained or confined so that its volume is not
permitted to change in response to changes in
its temperature.
• To provide for the normal expansion and
contraction of materials that is driven by
changes in temperature, expansion joints are
utilized in various structures.
Coefficient of Expansion
• When solids and liquids are heated and their
temperatures increases, their volumes also
change a fixed quantity for each on degree rise
in temperature.
• The coefficient of expansion differs among
different materials. It is also known to vary for
the same substance, based on the temperature
at which the heat transfer is occurring.
Paradox of Water
• One of the few exceptions to the direct
relationship between temperature and volume
is water.
• As warm water is cooled, its volume decreases
as expected, until its temperature drops to
39.2°F.
• At this temperature water achieves its
maximum density, and smallest volume.
Paradox of Water
• As the water cools past 39.2°F it begins to
expand , this expansion continues as long as
the temperature continues to drop toward it’s
triple point 32°F.
• At the triple point temperature, the liquid
water begins to change phase into a solid,
continuing to expand.
• 1 ft3 of water will freeze to 1.085 ft3
Paradox of Water
• Although the expansion of water appears to
contradict the temperature-volume
relationship this is not the case.
• The average distance between the cooling
molecules continues to decrease as the
temperature drops. But a physical rather than a
thermal expansion occurs as the water
molecules arrange into a crystalline structure.
Relationship Between
The Properties of Gases
• The reaction of gases to changes in thermal
energy is much more complex than that of
liquids and solids.
• This complexity requires the use of several
equations to determine their properties.
• The change in volume experienced by gases as
they are heated or cooled is much greater than
that experience by solids or liquids.
Relationship Between
The Properties of Gases
• The complexity of the change is a consequence
of the lack of structure and weak molecular
attractions of gas molecules as compared to
those of solids and liquids.
• Therefore, several gas laws were developed
that are used to predict the response of a gas
to changes in its environment.
Relationship Between
The Properties of Gases
• Through the application of these gas laws,
technicians can predict the response of
refrigeration processes that use gases and
vapors as their working fluids.
• Remember that a gas completely fills its
containing vessel so that any change in volume
produces corresponding changes in its
temperature and pressure. The following
equations are for constant processes.
Constant Temperature
Processes
• In 1662, Robert Boyle determined that if the
temperature of a gas was kept constant,
changes in its absolute pressure and volume
were indirectly related to each other.
• When a constant temperature gas was
compressed, its absolute pressure increased in
proportion to the reduction in its volume.
Constant Temperature
Processes
• Conversely, when a gas was expanded at a
constant temperature, its absolute pressure
decreased in proportion to the increase in its
volume.
• This discovery led to the publishing of the first
of three ideal gas laws. The law is named after
Robert Boyle and is called Boyle’s law for
constant temperature processes.
Constant Temperature
Processes
• Any thermodynamic process that occurs in such
a manner that the temperature of the working
fluid is held constant, is called an isothermal
process.
• Since the molecules of any gas fly about
randomly at high velocities, they frequently
collide with one another and with the walls of
their container.
Constant Temperature
Processes
• Billions and billions of gas molecules strike the
interior walls at any instant in time.
• It is these molecular collisions that manifest
themselves as pressure exerted on the walls of
the containment vessel.
• The magnitude of the pressure generated by a
gas is a function of the frequency and the force
of the molecular impacts.
Constant Temperature
Processes
• There are several processes, that can increase
the pressure of a gas.
• When the number of molecules contained in a
volume of gas is increased, the number of
collisions also increases, this increases the
pressure in the vessel.
• The same reaction occurs when the number of
molecules remains the same but the volume
decreases.
Constant Temperature
Processes
• Engines and compressors are used to raise gas
pressure by trapping a fixed amount of gas in a
cylinder and reducing the volume by moving a
piston toward the cylinder head.
• As the piston reduces the volume available for
the gas, raising the number of molecular
collisions and the pressure in the cylinder.
Constant Temperature
Processes
• Another process that can be used to raise the
pressure of a confined gas is transferring heat
to the vessel.
• Since the force created by the molecule
colliding with its vessel’s wall is a function of its
velocity, raising the molecular velocity is
accomplished by raising its kinetic energy.
Constant Temperature
Processes
• The higher the temperature, the greater the
molecular velocity and the forces transmitted
during collisions with the vessel walls.
• In isothermal processes, the temperature and
its kinetic energy remains constant. Therefore,
differences in pressure can only occur if the
volume or the mass of the gas within the vessel
is altered.
Constant Temperature
Processes
• In accordance with Boyle’s law, if a gas is
allowed to expand in a constant temperature
process, changes in its volume and pressure are
inversely related.
• Since the kinetic energy of the gas remains
constant in isothermal expansion processes,
the decrease in pressure is the result of the
reduction in density of the gas as it expands to
fill the volume of the containment vessel.
Constant Temperature
Processes
• The decrease in density reduces the frequency
of molecular collisions, producing a
corresponding decrease in the gas pressure.
• Since gas cools as it expands, the isothermal
characteristic of the process can only be
maintained if heat is transferred to the gas
during an isothermal expansion process.
Constant Temperature
Processes
• The complementary response of an expansion
process occurs when a gas is isothermally
compressed.
• When a gas is compressed at a constant
temperature, the pressure increases in
proportion to the magnitude of the decrease in
gas volume.
Constant Temperature
Processes
• The reduction in volume of the containment
vessel causes a corresponding increase in the
density of the gas.
• As the density of the gas increases, the
frequency of collisions also increases,
generating a corresponding increase in
pressure.
Constant Temperature
Processes
• The average velocity and kinetic energy of the
molecules must remain unchanged in order to
maintain the relationship of Boyle’s law.
• Therefore, heat must be transferred from the
cylinder during an isothermal compression
process.
Constant Pressure
Processes
• In 1787 Jacques Charles discovered that if the
pressures of carbon dioxide, hydrogen, oxygen
and nitrogen were kept constant, they
expanded at predictable rates in response to an
increase in their temperature.
• Charles never published his findings, still this
relationship is called Charles’ law for constant
pressure processes.
Constant Pressure
Processes
• Any thermodynamic process that occurs in such
a way that the pressure of the working fluid is
held constant is called isobaric process.
• As thermal energy is added to the gas, its
temperature and volume increase in
accordance with Charles’ law.
• The heat transferred to the gas increases its
kinetic energy and the velocity of its molecules.
Constant Pressure
Processes
• The higher energy collisions increases the
pressure within the cylinder, consequently the
volume must expand to maintain the constant
pressure relationship.
• Heat must be transferred to or from the
cylinder in an isobaric process in order to
maintain the relationship between volume and
temperature, as described in Charles’ law.
Constant Pressure
Processes
• When thermal energy is removed from the
cylinder, the pressure in the cylinder begins to
decrease.
• The volume of the cylinder must then be
decreased to maintain the constant pressure
relationship.
Constant Volume
Processes
• Charles explored the relationship between
temperature and pressure in constant volume
processes.
• He found that when the volume of a process
remains constant, the pressure of the gas
changes in direct proportion to the change in
its temperature.
• Once again Charles never published his findings
Constant Volume
Processes
• In 1802 Joseph Gay-Lusaac repeated Charles’
gas experiments as he studied gases.
• His findings agreed with the earlier
unpublished work of Charles’.
• Gay-Lusaac published his data in 1809, and for
that reason Charles’ law of Constant Volume
Processes is also known as Gay-Lusaac’s law.
Constant Volume
Processes
• Any thermodynamic process that occurs in such
a way that the volume of the working fluid is
held constant is called an isometric process.
• In a constant volume process the volume of the
gas cannot change as it is heated or cooled,
therefore changes in the pressure can only be
caused by changes in its temperature.
Constant Volume
Processes
• As heat is added to the cylinder, the absolute
pressure of the gas increases in direct
proportion to the increase in the absolute
temperature of the gas.
• The response occurs because the addition of
heat increases the kinetic energy and velocity
of the gas molecules, thereby increasing the
force transmitted to the cylinder walls by
molecular collisions.
Constant Volume
Processes
• Conversely, when the gas in the cylinder is
cooled, its absolute pressure decreases in
direct proportion to the decrease in absolute
temperature.
• This occurs because the force and frequency of
molecular impingement on the walls of the
cylinder diminish as their velocity decreases.
AVOGADRO’S LAW
• In 1811, Amedeo Avogadro proposed that
equal volumes of different gases contain the
same number of particles when maintained at
the same pressure and temperature.
• It was later discovered that a volume of
0.79 ft3 at 32°F and 14.696 psia contains
approximately 6.02 x ���� or 602 billion trillion
particles
AVOGADRO’S LAW
• This number is called the Avogadro constant,
and is used as a measurement of quantity in
combustion analysis, gas measurements and
other chemical analysis.
• This quantity is called a mole of a substance,
one mole of any substance contains
6.02 x ���� elementary particles (atoms,
molecules, ion, electrons, etc.)
AVOGADRO’S LAW
• The symbol for Avogadro constant is a
lowercase letter n
• Moles are measured in mass units
(lbmol, kgmol)
The Ideal Gas Law
• The ideal gas law was developed by combining
the relationships in Boyle’s and Charles’ laws
along with Avogadro’s number into a single
formula.
• Combining Boyle’s and Charles’ laws yields the
following equation�����
�= �����
�
• This on equation is all that is needed to solve
Boyle’s and Charles’ law relationships.
Specific Gas Constant
• A gas constant is a property of a gas that
expresses the relationship that exists between
its absolute temperature, absolute pressure
and volume at a given state.
• The gas constant is a calculated value equal to
the product of the absolute pressure and
specific volume of the gas divided by its
absolute temperature.
Specific Gas Constant
• The result is known as the specific gas constant
of the gas and is depicted with an uppercase R.
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=
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Specific Gas Constant
• The mathematical result of the formula is
always the same for a particular gas because
increases in its absolute pressure and
temperature are offset by a corresponding
decrease in its specific volume.
• The specific gas constant is an extensive
property of a gas, meaning its quantity is based
on a unit mass of gas.
Universal Gas Constant
• A universal gas constant is a property of gasses
that has the same value. The universal gas
constant is equal to 1545 ft-lbf/lbmol-R or
8,314 J/kgmol-K.
• The symbol for the universal gas constant is *R
where the asterisk indicates the universal value
is being used in the equation.
Universal Gas Constant
• The universal gas constant is based on the
quantity relationship of gas molecules
discovered by Avogadro.
• Since there are equal numbers of particles in
one mole of a gas at a given volume,
temperature, and pressure, the only difference
between gasses must be caused by differences
in the configuration of their atoms.
Universal Gas Constant
• The only difference between gases happens to
be in the makeup of their molecular structure,
which is depicted in their mass or molecular
weight.
• The molecular weight of an atom is equal to its
atomic number, which is found on the periodic
table of elements.
Universal Gas Constant
• The specific gas constant of a gas can be
calculated by dividing the universal gas
constant (*R) by the molecular weight of a one
mole quantity of a gas.
• Oxygen has a molecular weight of 32,
therefore, its specific gas constant is equal to
1545 ÷ 32 = 48.3 lbf/lbm R
Ideal Gas
• Gases are highly superheated vapors.
• A gas is considered to behave in an ideal
manner when its pressure is very low and its
temperature is considerably higher than its
critical temperature.
• The critical temperature of a substance
indicates the highest possible temperature at
which the substance can exist as a liquid.
Ideal Gas
• Above the critical temperature there is no
longer any difference between the properties
of its liquid and gas phases
• At 14.696 psia oxygen liquefies at -297°F, as its
pressure is raised to 750 psi it can be liquefied
at - 182°F.
• Therefore, this is also the highest temperature
at which the gas can be condensed.
Ideal Gas
• - 182°F is the critical temperature for oxygen. If
oxygen exists at a temperature that is much
greater than - 182°F, it will behave as an ideal
gas, thereby adhering to Boyle’s and Charles’
laws.
• Conversely refrigerants do not behave as ideal
gases because they exist at temperatures that
are too close to their saturation temperatures.
Ideal Gas
• Their molecules are packed much closer and,
consequently they experience too much
interaction between their electrostatic forces.
• This produces the molecular equivalent of
friction, since the effects of friction cannot be
reversed, the vapor and its process are not
ideal.
Ideal Gas
• Therefore, the process and the gas cannot be
adequately described using the relationships
described in Boyle’s, Charles’ and the ideal gas
laws.
• The analysis of processes using non-ideal gases
must be performed using property tables to
determine their condition at specific states.