Download Z004 - THERMODYNAMICS

IDEAL GAS BEHAVIOR
THERMODYNAMICS OF GASES
Objective:
To understand how the Ideal Gas Law and
the laws of thermodynamics are used
together to fully understand the behavior of
gases.
Goals:
1.
2.
Students will know the 1st law of
thermodynamics
Students will be able to use the
Ideal Gas Law and the 1st law of
thermodynamics to make basic
calculations about gases under
varying conditions.
represents an overall kinetic energy of the
gas and is recognized as wind.
If the gas is enclosed in a cylinder there is
no wind but merely randomized molecular
motion. Thus all molecular motion is
internal energy.
Assuming that a gas stays in the gaseous
state without phase change, the amount of
energy required to cause a temperature
change is given by:
Q = MCT
(eq. 1)
Where:
Vocabulary:
Adiabatic, Isobaric, Isothermal, Isometric,
Internal Energy
Q = Energy (joules)
M = Mass (kg)
CP = Specific heat (CP, Cv)
T = Temperature (Absolute)
This is the change in internal energy.
Temperature and Internal Energy:
The internal energy of a gas varies directly
with the temperature of the gas. At absolute
zero (0 K), all molecular motion stops so
that there is no energy within the gas at this
point.
As the randomized speed of the molecule
increases so does the internal kinetic energy
of the gas molecules. This increase in
randomized kinetic energy is noted as an
increased temperature
Note: If molecular motion within a gas
sample is not randomized (in all directions)
and is instead all in a common direction, it
does not represent internal energy and it
does not affect the temperature. Instead, this
Note: Within the natural range of
temperatures, the specific heat of
atmospheric air is approximately 1.007
kJ/kg K. This means that it takes 1.007 kJ of
energy to raise 1 kg of air by 1 degree K.
Activity:
Students build Excel spreadsheet calculator
to determine the heat difference between
different temperatures with variables for
mass and specific heat.
1ST Law of Thermodynamics
The first law of thermodynamics states that
energy is neither created or destroyed. The
sum of all energies entering a system and all
energies leaving a system represents a
change in the total energy of a system.
Activity:
Students develop an Excel model to analyze
change of internal energy for a system and
the resulting temperature change.
In physics we generally group energy into
two forms: Heat and Work
In this equation, heat is defined as the total
of all energy entering or exiting the system
by any means except by direct compression
or expansion of the gas.
Isobaric Work on a Gas:
As we discussed earlier, work refers to
energy
specifically
associated
with
expanding or compressing a gas.
Consider a piston assembly as shown below.
Work is defined as the energy added to or
removed from a gas by either compressing
or expanding the gas (i.e. a piston assembly)
since this is the manner in which machines
typically extract useful work from a gas.
Force = F
With this understanding, we can write the
First Law of Thermodynamics as:
U = Q + W
Distance = D
(eq. 2)
Where:
U = Internal Energy
Q = Energy added or removed from a
system by any means except for
‘work’.
W = Work done by changing volume
(compressing or expanding a
cylinder).
Questions:
-What is the change in internal energy of a
gas if 2,000 joules of work are done on the
gas and 6,000 joules of work is allowed to
exit the system by cooling?
-The enclosed gas in the previous question is
.02 kg of atmospheric air. If the gas starts at
308 K what is its final temperature?
-How much heat is required to increase the
temperature of 1.2 kg of air isometrically by
30 deg C?
As a forec F pushes down on the piston
through a distance D it compresses the gas.
If the force is constant, then the work
required to compress the gas is:
W=FxD
Which is the definition of work from
classical mechanics.
The Force required is equal to the pressure
of the gas times the cross sectional area of
the piston. Once again, if pressure remains
constant, this becomes:
W=PxAxD
Note: A x D = change in volume, thus for an
isobaric process:
U = H + U
or
U = 0 + (-)
W = PV
(Eq 3)
yielding:
U < 0
For our system we use the convention that
work done on the system (compression) has
a positive value and work done by the
system (expansion) has a negative value.
Isothermal Work on a Gas:
An isothermal system presents another
unique situation. In this system the pressure
is not constant but varies inversely with the
volume. This lead to a work equation:
W = Pavg V
T I F F
a r e
Q
u ic k T im
( Un c o m
n e e d e d
P dV
e ™
a n d a
p r e s s e d )
d e c o m p r e s s o r
t o s e e t h is
p ic t u r e .
Summary:
-The internal energy of a gas is directly
related to the temperature of the gas.
-The first law of thermodynamics:
U = Q + W
(Eq. 4)
General Work on a Gas:
All processes are not isobaric; in fact, this is
an unusual system. The general solution
equation is:
W=
Since, for an ideal gas, internal energy is
directly proportional to temperature. Thus,
this represents a decrease in temperature.
(Eq. 5)
This is a mathematical formula that is
beyond the prerequisite knowledge for theis
course so we will restrict our calculations to
the two specific conditions covered here.
Adiabatic Espansion:
It is a fact that warm air rises yet, we also
know that air gets colder at higher altitudes.
The process by which air cools as it rises is
called adiabatic expansion.
As the air rises it does not lose heat
(adiabatic) but it does expand due to the
reduced pressure. Expanding air means that
work is being taken out of the system. Based
upon the 1st Law of Thermodynamics we
see that, with H = 0 and W = negative, we
have:
-Gases are compressed throu a variety of
processes. Specific processes of interest are:
Adiabatic,
Isobaric,
Isothermal,
Isometric
-Adiabatic expansion causes air to cool as it
rises and expands without losing heat.
Homework:
Students should develop a comprehensive
Excel model to analyze the temperature and
energy change of a gas for various heat and
work conditions. Students may select their
own variable parameters but are encouraged
to include as much versatility as possible.