Thermodynamics & Heat Transfer - Chapter 2. Introduction to Gases & Gas Laws (Part 2).pdf

Theory of gases, Gas Laws with examples

1. Mr. S.S.Sajane
BE(Mech), ME (Heat & Power Engineering)
Department of Mechatronics Engineering,
Sharad Institute of Technology College of Engineering,
Yadrav- Ichalkaranji.
SITCOE,Yadrav-Ichalkaranji. Mr.S.S.Sajane

Thermodynamics & Heat
transfer

2. Ideal Gases and Ideal Gas Processes:
SITCOE,Yadrav-Ichalkaranji. Mr.S.S.Sajane

3. Introduction:
The thermodynamic
system uses gas as a
working medium.
Study of gas behavior
with respect to
pressure, temperature,
other parameters is
important.
In this chapter, we are
going to study various
basic laws of ideal
gases and processes
according to which it
behaves.
SITCOE,Yadrav-Ichalkaranji. Mr.S.S.Sajane

4. Points Covered:
Concept of Ideal Gas.
Difference between Real Gas and Ideal Gas.
Assumptions of Ideal Gas.
Gas Laws
SITCOE,Yadrav-Ichalkaranji. Mr.S.S.Sajane

5. Concept of Ideal gases:
A perfect gas or an ideal gas is one which follows the gas laws at all ranges of pressure
and temperature.
An ideal gas have no forces of molecular attraction because at low pressure and high temperature molecules of gas are far away from each other and so there is no any
molecular attraction between them.
In nature no such gas exists but real gases follow these laws at low pressure and high
temperature or at both.
SITCOE,Yadrav-Ichalkaranji. Mr.S.S.Sajane

6. SITCOE,Yadrav-Ichalkaranji. Mr.S.S.Sajane

7. Assumptions of Ideal Gas:
A finite volume of gas contains large number of
molecules.
The collision of molecules with one another and with the walls of container is perfectly elastic.
The molecules are separated by large distances compared to their own dimensions.
The molecules do not exert forces on one another except when they collide.
SITCOE,Yadrav-Ichalkaranji. Mr.S.S.Sajane

8. Gas Laws:
Boyle’s law
Charle's law
Gay Lussac’s law
Avogadro’s law
The behavior of a gas, undergoing
any change is studied with respect
to its pressure, temperature and
volume. Its behavior is governed
by the following laws:
SITCOE,Yadrav-Ichalkaranji. Mr.S.S.Sajane

9. Boyle’s Law:
•Statement:
The absolute pressure exerted by a given mass of gas is
inversely proportional to the volume when the
temperature remains constant.
Mathematically,
•If ‘P’ is absolute pressure & ‘V’ is volume of gas then



PV= Constant

•If a gas changes its volume from V
1to V
2 and Pressure
from P
1 to P
2 at constant temperature,
P
1V
1=P
2V
2

10. Application :
•A diver experiences approximately one
additional atmosphere of pressure for
every 10 m of depth, due to the weight of
the surrounding water.
•For example at 40 m, the diver experiences
approximately 4 atm of pressure.
•If a diver holds his or her breath and rises
to the surface quickly, the outside pressure
drops to 1 atm.
According to Boyle’s law, what
should happen to the volume of air in
the lungs?
•Since the pressure is decreasing by a factor
of 4, the volume will expand by a factor of
4, causing damage to lungs.
Hence it necessary that the Diver always
exhale when rising!

11. Charle’s Law:
•Statement: It states that volume of a given mass of a
perfect gas varies directly as the absolute temperature
when pressure is constant.
Mathematically,
•If ‘T’ is absolute temperature & ‘V’ is volume of gas
then


•If a gas changes its volume from V
1to V
2 and
temperature from T
1 to T
2 at constant pressure,

12. •If we move a balloon from an ice water bath to a boiling water bath, its volume expands
as the gas particles within the balloon move faster (due to the increased temperature) and
collectively occupy more space.

13. As the temperature of the air increases, the
volume of the air also increases and
consequently, the density decreases. This
makes the envelope lighter than the
atmospheric air surrounding it and thus the
balloon will start to fly .
Tyres of untouched vehicles get deflated during
freezing winter days while get inflated in hot
summer days. This is because in winter due to
low temperatures, the air inside a tyre gets
cooler, and they shrink. While in hot days, the
air expands with temperature.
Hot Air Balloon Tyres

14. Like tyres, helium balloons also experience
expansion and contraction with change in
surrounding temperature. If you take a balloon out in
a snowy day, it crumbles. When the same balloon is
brought back to a warm room, it regains its original
shape.
In winters, the temperature of air decreases.
As a consequent, the temperature of the air
inside the body also decreases. Hence, the
volume of the air decreases with the
temperature. It shrinks the lungs and physical
activities like jogging becomes difficult in
freezing winter days.

15. Gay Lussac’s Law:
•Statement: It states that the pressure of a given mass of
gas varies directly with the absolute temperature of the
gas, when the volume is kept constant.
•Mathematically, it can be written as



•For comparing the same substance under two different
sets of conditions, the law can be written as:

16. If the valve malfunctions then the pressure inside the cooker
increases with its temperature at constant volume. This high
pressure may rupture the cooker and may lead to an
unfortunate accident .
In hot summer days, the inflated tyres of vehicles may burst.
The bursting of tyres is caused by Gay-Lussac's law. The
inflated tyres are under high pressure. When the temperature of
the air rises, the pressure of the gas in the tubes increases. After
an unbearable point, the tyres fracture.

17. The electric water heater is similar to the pressure cooker.
The cold water is heated by the heating filaments inside
the heater. The hot water generated is released through the
outlet nozzle. Modern electric heaters automatically
regulate the temperature of water. When the system and
pressure-relief valve malfunctions, the steam is generated
by continuous power supply. This steam can damage the
heater. If the pressure of the steam exceeds the tolerable
limit, the heater may burst.

18. Avogadro’s Law:
Statement: It states that equal volumes of gases at the same temperature and pressure
contain equal numbers of molecules.

19. Avogadro’s Law:
• The law can be written as:


where
V is the volume of the gas;
n is the amount of substance of the gas (measured in moles);
k is a constant for a given temperature and pressure.
• This law describes how, under the same condition of temperature and pressure,
equal volumes of all gases contain the same number of molecules.
• For comparing the same substance under two different sets of conditions, the law can be
usefully expressed as follows:

20. Avogadro’s Law:
If the amount of gas in a container is increased, the volume
is increased.
As you decrease the amount of gas, the volume of the container also decreases likewise.
As per Avogadro's theory the number of atoms or molecules in one mole of a substance, equal to 6.023 × 10
23
.
Just like a dozen is 12 things, a mole is simply Avogadro's number of things.

21. Combined Laws:

22. Equation of State:
•The mathematical equation which describes the relationship between pressure,
volume, temperature for a perfect gas, is known as Equation of state.

•Derivation:
Consider 1 Kg of gas which changes its state from P1, V1, T1 to P2,
V2, T2 by two processes,

a) Constant Pressure Process ( 1-A)
b) Constant Temperature Process ( A-2)

As shown in Figure,

23. •During constant pressure process, volume changes from V1 to VA and during
constant temperature process volume changes from VA to V2.
Process 1-A, P = C, Applying Charle’s law we get,



•Process A-2, T = C, Applying Boyle’s law we get,

24. Characteristic Gas Equation:
For ‘m’ Kg mass


Where,
P= Pressure in N/m2
V = volume in m3
m= Mass of gas in Kg
T= temperature in K
R= Characteristic Gas Constant in J/Kg K
PV= mRT

25. Characteristic Gas Constant-R :
•The value of R is called Characteristic gas Constant.
• Its value is different for different gases,
• For AIR, R= 287 J/Kg K
• For Oxygen, R= 259.8 J/kg k

•Unit= J/Kg K

26. Universal Gas Constant/Molar Constant(R):
•Value of R is varies for each gas so for uniformity R is replaced by Universal gas
Constant, which is product of molecular weight & characteristic gas constant.

•Let, M= molecular weight of gas in Kg,
R = characteristic gas constant for same gas
•Then,
R = R X M

•Unit = J/Kg-mole K
•Value: 8314.3 J/Kg -mole K

27. THANK YOU