thermodynamics lecture 1 sengel bkkkkkook

Today’s lecture….
• Composition of non reacting gases.
• Mole fraction.
• Mass fraction.
• Volume fraction.
• Delton’s Law of partial pressure.
• Amagat’s Law

Composition of a gas mixture
• The composition of a gas mixture refers to the relative amounts or
proportions of different gases that make up the overall mixture. This
composition is often expressed using various metrics such as mole fraction,
mass fraction, or volume fraction. Let's explore an example to illustrate the
concept of gas mixture composition:
• Air is a common example of a gas mixture. It is composed of several gases,
with nitrogen (N₂) and oxygen (O₂) being the primary components. Other
gases, such as carbon dioxide (CO₂), argon (Ar), and trace amounts of other
gases, are also present.

Perfect gases
• Perfect gases generally refers to an idealized model of gases that follows ideal
gas laws. In the ideal gas model, gases are assumed to consist of particles
(atoms or molecules) that are in constant, random motion, and the
interactions between these particles are negligible.
𝑷𝑽 = 𝒏𝑹𝑻
• It's important to note that real gases deviate from ideal behavior under
certain conditions, such as at high pressures or low temperatures.
• In reality, no gas is truly perfect according to the ideal gas laws under all
conditions.

Properties of an ideal gas mixture
• Each gas in the mixture behaves independently of the others.
• The total pressure of the ideal gas mixture is the sum of the partial
pressures of each gas.
Ptotal = P1+ P2 + P3 +……..+ Pn
• The total volume of the ideal gas mixture is the sum of the volumes that
each gas would occupy individually at the same temperature and
pressure.
• Ideal gas mixtures assume that there are no intermolecular forces or
interactions between gas molecules.
• This implies that the gases do not condense into liquids or exhibit
deviations from ideal behavior.

Mole Fraction
• Mole fraction ( 𝑥𝑖) is the ratio of moles of a specific gas to the total moles in the
mixture.
𝑥𝑖 =
𝑛𝑖
𝑛𝑡𝑜𝑡𝑎𝑙
• Mole fractions are essential for quantifying the proportion of each gas in the
mixture, aiding in comprehensive composition analysis.
• Mole fraction of 𝑁2 (𝑥𝑁2
) =
moles of N₂ (𝑛𝑁2)
total moles in air (𝑛𝑡𝑜𝑡𝑎𝑙)
• Mole fraction of 𝑂2 (𝑥𝑂2
) =
moles of O₂ (𝑛𝑂2)
total moles in air (𝑛𝑡𝑜𝑡𝑎𝑙)

Mass fraction
• Mass fraction refers to the proportion of the total mass of a specific gas
component in a mixture of gases. The mass fraction is a measure of the
concentration of a particular gas within the overall gas mixture. It is
calculated by dividing the mass of the individual gas (𝑚𝑖) by the total mass
(𝑚𝑡𝑜𝑡𝑎𝑙) of the gas mixture.
𝑤𝑖 =
𝑚𝑖
𝑚𝑡𝑜𝑡𝑎𝑙
• For a mixture of non-reacting gases, the sum of the mass fractions of all
individual gases should equal 1. This reflects the fact that the total mass of
the mixture is distributed among the different gas components.

Volume Fraction:
• The volume fraction is the ratio of the volume of each gas to the total
volume of the mixture.
• In the case of air, the approximate composition by volume is often
given as about 78% nitrogen, 21% oxygen, 0.04% carbon dioxide, and
trace amounts of other gases.

Dalton's Law of Partial Pressures
• According to Dalton's Law, the total pressure exerted by a mixture of
non-reacting gases is the sum of the partial pressures of individual
gases.
Ptotal = P1+ P2 + P3 +……..Pn
• This law is particularly useful when dealing with gas mixtures,
providing a straightforward method to calculate the contribution of
each gas to the total pressure.

Example
• Suppose you have a container that contains a mixture of three non-
reacting gases: nitrogen (N₂), oxygen (O₂), and carbon dioxide (CO₂). Each
gas exerts its own pressure within the container.
• According to Dalton's Law:
Ptotal=PN₂+ PO₂+ PCO₂
PN₂= 400 kPa; PO₂ = 300 kPa; PCO₂= 300 kPa
Ptotal= 400 kPa + 300 kPa + 300 kPa = 1000 kPa

Problem:1
• You have a container containing a mixture of two non-reacting gases:
oxygen (O₂) and nitrogen (N₂). The total pressure in the container is
800 kPa, and the mass fraction of oxygen in the mixture is 0.4.
Determine:
• The mass fraction of nitrogen in the mixture?
• The mass of oxygen in the container if the total mass of the mixture is
5 kg?

Solution
• Mass Fraction of Nitrogen (𝑤𝑁2
):
𝑤𝑁2
+ 𝑤𝑂2
= 1
𝑤𝑁2
= 1−0.4 = 0.6
• Mass of Oxygen in the Container:
𝑤𝑂2
=
𝑚𝑂2
𝑚𝑂2
= 0.4×5

Problem:2
• You have a container containing a mixture of three non-reacting gases:
hydrogen (H₂), carbon dioxide (CO₂), and nitrogen (N₂). The partial
pressures of these gases are as follows: PH₂= 150kPa; PCO₂= 200 kPa;
PN₂= 100 kPa. The molar masses of the gases are: MH₂ = 2 g/mol;
MCO₂= 44 g/mol; MN₂ = 28 g/mol. if the container volume is 5 L and the
temperature is 300 K. Calculate:
• The mole fraction of each gas in the mixture.
• The mass fraction of each gas in the mixture.

Solution
𝑥𝐻2
=
𝑛𝐻2
𝑛𝑡𝑜𝑡𝑎𝑙
• Use the ideal gas law to find the moles of each gas (ni):
𝑛𝑖=
𝑃𝑖𝑉
𝑅𝑇
• Where R=8.314 J/(mol K) Is the ideal gas constant.
𝑤𝐻2 =
𝑚𝐻2
𝑚𝑖 = 𝑛𝑖 × 𝑀𝑖

Amagat's law
• The volume occupied by a mixture of non-reacting gases is equal to the sum
of the volumes of the individual gases at the same temperature and pressure
as the mixture.
𝑉𝑡𝑜𝑡𝑎𝑙 = 𝑖=1
𝑛
𝑉𝑖
• This law is applicable on the non-reacting gases where there are no significant
intermolecular forces between the gas molecules.
• It's essential to note that Amagat's law is most accurate under conditions
where gases behave ideally, and it becomes less precise under extreme
conditions (high pressure, low temperature) or when gases have significant
interactions with each other.

Example
• Let's say you have a container of nitrogen gas (N₂) and a container of argon
gas (Ar). According to Amagat's law, the total volume of the gas mixture,
assuming ideal behavior, would be the sum of the volumes of nitrogen and
argon individually.
𝑽𝒕𝒐𝒕𝒂𝒍 = 𝑽𝑵𝟐
+ 𝑽𝑨𝒓
• It's essential to note that Amagat's law is most accurate under conditions
where gases behave ideally, and it becomes less precise under extreme
conditions (high pressure, low temperature) or when gases have significant
interactions with each other.

Adiabatic mixture of perfect gases
• The adiabatic mixture of perfect gases refers to a scenario where a mixture of
perfect gases undergoes an adiabatic process. An adiabatic process is one in
which there is no heat exchange with the surroundings.
𝑃𝑉𝛾
= 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
• 𝛾 = 𝐶𝑉
𝐶𝑃
represents the ratio of the specific heat at constant pressure to the
specific heat at constant volume.
• For a mixture of perfect gases, each gas component in the mixture follows its
own adiabatic process, and the overall behavior is determined by the
combined effect of these individual processes.

• The adiabatic process equations are commonly used to analyze the changes in
temperature, pressure, and volume of a gas mixture when no heat is
transferred to or from the system.
• This can be relevant in various applications, such as in the analysis of
processes in internal combustion engines, compressors, and other
thermodynamic systems where heat exchange with the surroundings is
minimal.
• It's worth noting that the adiabatic process assumes that the system is
insulated from its surroundings, and any changes in internal energy are solely
due to work done on or by the system.

Adiabatic Compression in a Compressor:
• Initial State:
• Air enters the compressor at a certain temperature, pressure, and volume.
• The compressor compresses the air adiabatically, meaning that no heat is exchanged
with the surroundings.
• Compression:
• As the air is compressed, its volume decreases, and its pressure and temperature
increase.
• The adiabatic compression process can be described by the adiabatic equation 𝑃𝑉𝛾 =
𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡, where P is the pressure, V is the volume, and γ is the ratio of specific heats.
• Final State:
• The air exits the compressor at a higher pressure, temperature, and potentially a
different volume.

thermodynamics lecture 1 sengel bkkkkkook

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