Transcript Ideal gas - Nutley Schools

Ideal gas
• Assumptions
1. Particles that form the gas have no volume
and consist of single atoms.
2. Intermolecular interactions are vanishingly
small.
Ideal gas
Equations of state
PV=NkT
P= pressure
V= volume
N=number of particles of gas
k= Boltzmann Constant= 1.38x10-23J/K
K=Kelvin temperature
Ideal gas
Equations of state
PV=nRT
P= pressure
V= volume
n=number of moles of gas
R= Universal Gas Constant=
K=Kelvin temperature
8.31
J
mol K
Ideal gas
Avogadro’s number
molecules
N A  6.022 x10
mol
23
Ideal gas
Relationship between Avogadro’s number,
Universal Gas constant, and Boltzmann
constant.
R  k  NA
Kinetic –molecular theory
1. Many molecules are in a container and they
behave like point particles.(No volume)
2. The molecules move around randomly, and
obey Newton’s laws.
3. The only interactions that the molecules
undergo are elastic collisions with each other
and the walls of the container.
Kinetic –molecular theory
Pressure is a result of the molecules colliding
with the walls of the container. As the number
of molecules or thir average speed increases,
the pressure increases.
Kinetic –molecular theory
Results of kinetic-molecular theory.
3
1 2
K av   mv   kT
2
av 2
T  Kelvin temperature
Kinetic –molecular theory
Results of kinetic-molecular theory.
3kT
3RT
vr ms 

m
M
T  Kelvin temperature
m= the mass of one molecule
M= the mass of one mole of molecules
Kinetic –molecular theory
Internal energy of an ideal monatomic gas..
3
3
U  NkT  nRT
2
2
T  Kelvin temperature
N= number of molecules
n= number of moles
Kinetic –molecular theory
Other gas laws – the amount of gas does not
change
Boyle's Law - applies at constant temperature
P1V1 =P2 V2
Charles' Law - applies at constant pressure
V1 V2

T1 T2
Combined Gas Law
PV
P2V2
1 1

T1
T2
Laws of Thermodynamics
The first Law of Termodynamics –
If U is the internal energy of a system, than
DU=Q-W.
If Q>0 System gains heat
If Q<0 System loses heat
If W>0 Work is done by the system
If W<0 Work is done on the system
Laws of Thermodynamics
The first Law of Thermodynamics –
If U is the internal energy of a system, than
DU=Q-W
Table 18-1
Signs of Q and W
Q positive
System gains heat
Q negative
System loses heat
W positive
Work done by system
W negative
Work done on system
Figure 18-1
The Internal Energy of a System
Figure 18-2
Work and Internal Energy
Laws of Thermodynamics
At constant pressure, the work done by or on a
system is
W=PΔV
The area under a PV curve represents work. If a
process occurs at a constant volume, the work
done during the process is 0.
Figure 18-5
A Constant-Pressure Process
Example 18-2
Work Area
Laws of Thermodynamics
Isothermal processes – these are processes that
take place at a constant temperature.
PV=constant
Figure 18-8
Isotherms on a PV Plot
Laws of Thermodynamics
Adiabatic processes – these are processes that
take place without heat entering or leaving the
system.
DU  Q  W
During an adiabatic process Q=0 and
DU  Q  W  W
Figure 18-9
An Isothermal Expansion
Figure 18-10a
An Adiabatic Process
Figure 18-10b
An Adiabatic Process
Conceptual Checkpoint 18-2 Page 578
Which is the adiabatic curve?
Figure 18-14
A Comparison Between Isotherms and Adiabats
Laws of Thermodynamics
• A heat engine is a device that converts heat
into work.
• It operates between at least two temperatures
referred to as the hot reservoir and the cold
reservoir.
• A classic example is a steam engine.
Example 18-6
Heat into Work
Laws of Thermodynamics
Steam engine
Laws of Thermodynamics
Sadi Carnot (1796-1832) developed a theorem
that allows on to calculate the theoretical
efficiency of a heat engine operating between
two temperatures. He assumed that in an ideal
engine all processes are reversible. If this were
true, the engine would have maximum
efficiency, and all ideal engines operating
between those two temperatures would have the
same efficiency.
Laws of Thermodynamics
Maximum efficiency of a heat engine.
emax
Tc
 1
Th
Where : emax = maximum efficiency
Tc  temperature of the cold reservoir in Kelvins
Th  temperature of the hot reservoir in Kelvins
Laws of Thermodynamics
This expression applies to ideal (Carnot)
engines. The efficiency of a real engine will
always be less.
Under what conditions would a ideal engine
have an efficiency of 1?
Active Example 18-2
Find the Temperature
Active Example 18-3
Find the Work
Laws of Thermodynamics
Recollect – when two objects are in thermal
contact heat can flow between them.
The second law of thermodynamics.
When two objects at different temperatures
are brought into thermal contact, the
spontaneous flow of heat is always from the
high temperature object to the low
temperature object.
Laws of Thermodynamics
Entropy S is a thermodynamic quantity whose
change defined as the heat transferred during a
reversible process divided by the Kelvin
temperature
For a reversible process:
Q
DS 
T
J
unit :
K
Laws of Thermodynamics
During an irreversible process the entropy of the
universe is increased. During an ideal reversible
process the entropy of the universe remains
unchanged.
Laws of Thermodynamics
Example:
0.125kg of ice melts at 0oC. The heat absorbed
during the process is 4.19x104J.
What is the entropy change for the process?
Example 18-9
Entropy Is Not Conserved!
Calculate the
entropy change
for the process.
Laws of Thermodynamics
For an irreversible process,
entropy will always increase.
Unlike energy, entropy is not
conserved.
Laws of Thermodynamics
Third Law of Thermodynamics
It is impossible to lower the
temperature of an object to absolute
zero in a finite number of steps.