Download Chapter 7: Ideal Gases

Summary of Energy Topics
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Chapter 1: Thermodynamics / Energy Introduction
Chapter 2: Systems & Processes
Chapter 3: Work, Energy, Temperature & Heat
Chapter 4: Work Processes of Closed Systems
Chapter 5: Thermodynamic Properties
Chapter 6: Steam Tables
Chapter 7: Ideal Gases
Chapter 8: Conservation of Mass & Energy
Chapter 9: 1st Law of Thermodynamics
Chapter 10: Steady Flow Energy Equation
Chapter 11: Heat Engines and Reversibility
Chapter 12: 2nd Law of Thermodynamics
Chapter 13: Entropy
Chapter 14: General Energy
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
• We have steam tables for water, but what about other gases?
• Ideal gases uses a simple equation to describe a gas over a
wide range of its possible thermodynamic states
• Assumes that the specific heats cp and cv (specific heat
capacity at constant pressure and volume respectively) are
constant, thus changes in specific internal energy u or the
specific enthalpy h can be calculated without thermodynamic
tables.
• Most gases, such as air or hydrogen, can be regarded as 'ideal
gases' like at:
– temperatures well above their respective critical temperatures
– pressures well below their respective critical pressures.
– at very low pressures
Chapter 7: Ideal Gases & Associated Laws
Ideal Gases: Do not attract or repel each other
• At normal temperatures and pressures most gases act
similar to ideal gases.
Chapter 7: Ideal Gases & Associated Laws
Khan Academy
Chapter 7: Ideal Gases & Associated Laws
THE IDEAL GAS EQUATION
pv= RT or pV=mRT
where R is known as the specific gas constant
(dry air R = 286.9 J /kg.K)
R depends only on the molar mass
P=pressure
v=specific volume
V=volume
m=mass
R=gas constant for
a particular gas
T=temperature in
absolute units
of the gas, i.e.
Specific Gas Constant:
where
is known as the universal gas constant (= 8.3145 kJ/kmol.K). The
molar mass, has the units of kg/kmol.
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
1bar = 105 Pa
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
T2 = 20˚C
= 273.15+20
= 293.15K
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
CONVERT
To SI…N/m2
Chapter 7: Ideal Gases & Associated Laws
Heat Capacity: amount of heat required to change the temperature of
a substance by a given amount
Joules Law:
It is not dependent on pressure or volume.
PV=mRT
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Both a function
of Temperature
Chapter 7: Ideal Gases & Associated Laws
INTERNAL ENERGY AND ENTHALPY DIFFERENCES:
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
Mass x specific internal energy
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
Just calculated
PV=mRT
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
For any process, change in internal energy: (U2- U1) = mCv(T2- T1)
For any process, change in internal energy: (H2- H1) = mCp(T2- T1)
The heat energy required to
raise the temperature of mass
m from t1 to t2 at constant
volume
The heat energy required to
raise the temperature of mass
m from t1 to t2 at constant
pressure
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
IDEAL GAS PROCESSES
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
IDEAL GAS PROCESSES
constant
Upside down
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
IDEAL GAS PROCESSES
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
IDEAL GAS PROCESSES
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
Assume mass doesn’t change  Adiabatic Process
PV=RT
H=U+PV
(u2- u1) = Cv(T2- T1)
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
EXAMPLE : Adiabatic compression
A common example of adiabatic compression is the
compression stroke in a petrol engine. Calculate the
temperature of the compressed gas in the engine
cylinder under the following conditions: that the
uncompressed volume of the cylinder is 1 litre, that
the gas within is nearly pure nitrogen (thus a
diatomic gas with five degrees of freedom; so γ =
7/5), and that the compression ratio of the engine is
10:1 (that is, the 1 litre volume of uncompressed gas
will compress down to 0.1 litre when the piston goes
from bottom to top. The uncompressed gas is at
approximately 300 K, and a pressure of 1 bar or
0.1MPa (100,000 Pa), (typical sea-level atmospheric
pressure).
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
EXAMPLE : Adiabatic compression
A common example of adiabatic compression is the compression stroke in a petrol engine. Calculate the temperature of the compressed
gas in the engine cylinder under the following conditions: that the uncompressed volume of the cylinder is 1 litre, that the gas within is
nearly pure nitrogen (thus a diatomic gas with five degrees of freedom; so γ = 7/5), and that the compression ratio of the engine is 10:1
(that is, the 1 litre volume of uncompressed gas will compress down to 0.1 litre when the piston goes from bottom to top. The
uncompressed gas is at approximately 300 K, and a pressure of 1 bar or 0.1MPa (100,000 Pa), (typical sea-level atmospheric pressure).
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
EXAMPLE : Adiabatic compression
A common example of adiabatic compression is the compression stroke in a petrol engine. Calculate the temperature of the compressed
gas in the engine cylinder under the following conditions: that the uncompressed volume of the cylinder is 1 litre, that the gas within is
nearly pure nitrogen (thus a diatomic gas with five degrees of freedom; so γ = 7/5), and that the compression ratio of the engine is 10:1
(that is, the 1 litre volume of uncompressed gas will compress down to 0.1 litre when the piston goes from bottom to top. The
uncompressed gas is at approximately 300 K, and a pressure of 1 bar or 0.1MPa (100,000 Pa), (typical sea-level atmospheric pressure).
Dr. Joseph Stokes
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
EXAMPLE
Air at 1 bar and 20°C in a closed cylinder is compressed
adiabatically in an equilibrium process to 5 bar, in order
to pump up a dinghy. Determine the final temperature in
°C, the compression ratio (i.e. V1/V2) and the work done
on the air per unit mass.
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Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
EXAMPLE
Air at 1 bar and 20°C in a closed cylinder is compressed
adiabatically in an equilibrium process to 5 bar, in order
to pump up a dinghy. Determine the final temperature in
°C, the compression ratio (i.e. V1/V2) and the work done
on the air per unit mass.
Dr. Owen Clarkin
School of Mechanical & Manufacturing Engineering
Chapter 7: Ideal Gases & Associated Laws
EXAMPLE
Air at 1 bar and 20°C in a closed cylinder is compressed adiabatically in an equilibrium process to 5 bar, in order
to pump up a dinghy. Determine the final temperature in °C, the compression ratio (i.e. V1/V2) and the work done
on the air per unit mass.
Dr. Joseph Stokes
School of Mechanical & Manufacturing Engineering