Fluid Mechanics with teacher's notes

Section 9-4
Demonstration 10
Temperature, pressure,
and volume
Purpose Demonstrate that
the same amount of gas occupies
a larger volume at a higher
temperature.
Materials Pyrex flask, balloon,
water, Bunsen burner, goggles
CAUTION Be sure to wear safety
goggles at all times when operating
the Bunsen burner, and use
tongs when handling the heated
glassware.
Procedure Place a small amount
of water in the flask, and cap it
with the balloon. Emphasize that
no gas can flow in or out of the
flask or the balloon. Ask students
what the air volume is in this
closed system (about equal to that
of the flask). Heat the flask until
the balloon expands (no need to
let water boil). Have students estimate
and record the balloon’s
approximate size. Ask them how
much air is in the flask now (same
volume, but fewer molecules) and
in the balloon and flask together
(same amount as before, but in a
larger volume). Place the balloon
under cold water (not the flask, to
avoid breakage) to return it to its
original size.
338
9-4 SECTION OBJECTIVES
• Define the general properties
of an ideal gas.
• Use the ideal gas law to
predict the properties of
an ideal gas under different
conditions.
Figure 9-16
The balloon is inflated because the
volume and pressure of the air
inside are both increasing.
338
Chapter 9
9-4
Properties of gases
GAS LAWS
When the density of a gas is sufficiently low, the pressure, volume, and temperature
of the gas tend to be related to one another in a fairly simple way. In
addition, the relationship is a good approximation for the behavior of many
real gases over a wide range of temperatures and pressures. These observations
have led scientists to develop the concept of an ideal gas.
Volume, pressure, and temperature are the three variables that completely
describe the macroscopic state of an ideal gas. One of the most important equations
in fluid mechanics relates these three quantities to each other.
The ideal gas law relates gas volume, pressure, and temperature
The ideal gas law is an expression that relates the volume, pressure, and temperature
of a gas. This relationship can be written as follows:
IDEAL GAS LAW
PV = Nk BT
pressure × volume =
number of gas particles × Boltzmann’s constant × temperature
The symbol k B represents a constant called Boltzmann’s constant. Its value
has been experimentally determined to be 1.38 × 10 −23 J/K. Note that when
applying the ideal gas law, you must express the temperature in the Kelvin
scale (see Section 9-2). Also, the ideal gas law makes no mention of the composition
of the gas. The gas particles could be oxygen, carbon dioxide, or any
other gas. In this sense, the ideal gas law is universally applicable to all gases.
If a gas undergoes a change in volume, pressure, or temperature (or any
combination of these), the ideal gas law can be expressed in a particularly useful
form. If the number of particles in the gas is constant, the initial and final
states of the gas are related as follows:
N1 = N2 P
⎯
1V1
⎯ = ⎯
T1
P2V2
⎯
T2
This relation is illustrated in the experiment shown in Figure 9-16. In this
experiment, a flask filled with air (V 1 equals the volume of the flask) at room
temperature (T 1) and atmospheric pressure (P 1 = P 0) is placed over a heat
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