principles of refrigeration chapter 7

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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�������

���

=

�����

��� Imperial

•�

=

�

�����

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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.