Properties of gases, 2110006, Elements of Mechanical Engineering

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Index

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Properties Of Gases
•Gases may be compressed
•Gases expand when less pressure is applied
•Gases can be mixed
•Gases expert a constant pressure on its container walls
•Gases have low densities

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Boyle’s Law
• Pressure is inversely proportional to the volume and can be written as:
• P=pressure in N/m2
• V=volume in dm3
• k=constant
• This is more usually written as:
• Pressure=constant
volume
• PV=k

5. Boyle’s Law

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Boyle’s Law
• Graphing Boyle’s results

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Charles’s law
When the pressure on a sample of a dry gas
is held constant, the Kelvin temperature and
the volume will be directly related.
this directly proportional relationship can be written as:
or
where:
V is the volume of the gas
T is the temperature of the gas (measured in Kelvin).
k is a constant.

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Charles’s law
• Graphing data for several gases

9. Charle’s Law

10. Gay Lussac Law
• It states that the volume of a given mass of an ideal gas
is directly propotional to its absolute temperature if the
pressure of gas is kept constant.

11. Gay Lussac Law

12. Gay Lussac Law

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From the general equation PV = nRT we get:
where P is pressure, V is volume, n is amount, and T is temperature.
As pressure is defined as force per unit area, the gas equation can also be
written as:
Area and volume are (length)2 and (length)3 respectively. Therefore:
Since force × length = work:
Specific Gas Constant

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• Volume and moles are directly proportional.
– If one increases the other increases
– constant temperature and pressure
• Another way of stating Avogadro’s Law is
V1 = V2
n1 n2
(constant temperature and pressure)
Avogadro’s law
or
•Avogadro's law states that, "equal volumes of all gases, at the
same temperature and pressure, have the same number of
molecules".

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Processes of Ideal Gas
1. Isochoric-----Constant Volume process

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For a constant volume process, the addition or removal of heat will lead to a
change in the temperature and pressure of the gas, as shown on the two graphs
above.
Substitute into
Cv 
2
22
1
11
T
vp
T
vp

2
2
1
1
T
p
T
p


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using the definition of the specific heat at constant volume
to replace dU in the first law.
The technical work done
dTmCQ V

2
1
T
T
V dTCmQ
 
2
1
)( 21
p
p
t ppvvdpw

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2.Isobaric-----Constant Pressure

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For a constant pressure process, the addition or
removal of heat will lead to a change in the
temperature and volume of the gas, as shown on
the two graphs above.
Substitute intoCp 
2
22
1
11
T
vp
T
vp

2
2
1
1
T
v
T
v


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Work done and Heat Transferred
pdvdTcq v  )( pvddTcq v 
dhq 
The amount of heat added to a closed system during a
constant pressure process equals to the increase in enthalpy.

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3.Isothermal Compression and Expansion

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For a constant temperature process, the addition or
removal of heat will lead to a change in the volume
and pressure of the gas, as shown on the two graphs
above.
Substitute into
CT 
2
22
1
11
T
vp
T
vp

2211 vpvp 

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Work Done and Heat Transferred
In an isothermal process, the temperature is constant. Applying the first law of
thermodynamics to this closed process
For an ideal gas, the internal energy is a function of temperature only, and since the
temperature is constant, then dU is zero and
pdvdTcq v 
pdvwq  

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4.Adiabatic Process

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Process equation
Quasi-static, adiabatic process for an ideal gas
δq = cvdT + pdv and δq = cpdT – vdp
then cvdT = -pdv and cp dT =vdp
therefore
then
finally, we arrive at the very useful expression
from which it can also be shown that
dv
dp
p
v
c
c
v
p
 or
p
dp
v
dv
k 
0lnln
1
2
1
2

p
p
v
v
k or 1
11
22
k
k
vp
vp

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Work Done and Heat Transferred
When the temperatures at the start and end of the
process are known, the work done is calculated
from
1
)(
)(
1
1
)(
21
2211
2
1
2
1
12








k
TTR
vpvp
k
dv
v
pv
pdvw
TTcpdvw
k
k
v
)(
1
)(
1
)(
)(
21
12
21
2
1
2
1
TTR
k
k
TTR
k
TTR
pvdpdvw
vdpw
t
t











kwwt 
0Q

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5.Polytrophic Process
• Many processes can be approximated by the law:
• where,
P Pressure,
v Volume,
n an index depending on the process type.

28. When the temperatures at the start and end of the
process are known, the work done is calculated
from
Work Done and Heat Transferred
1
)(
)(
1
1
21
2211
2
1
2
1








n
TTR
vpvp
n
dv
v
pv
pdvw
pdvw
n
n

)(
1
)(
1
)(
)(
21
12
21
2
1
2
1
TTR
n
n
TTR
n
TTR
pvdpdvw
vdpw
t
t











nwwt 

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