An important property of any gas
(including air) is temperature. We have some experience with
temperature that we don't have with properties like viscosity
and compressibility. We've heard meteorologists give the daily
value of the temperature of the atmosphere (15 degrees Celsius, for
example). We know that a hot object has a high temperature, and a
cold object has a low temperature. And we know that the temperature
of an object can change if we heat the object or cool it.
Scientists, however, must be more precise than simply describing
an object as "hot" or "cold." An entire branch of physics, called
thermodynamics, is devoted to studying the
temperature of objects and the flow of heat
between objects of different temperatures. We are including some
fundamentals of thermodynamics at the Wright brothers web site to help you
better understand the fundamentals of
engines.
There are two ways to look at temperature: (1) the small scale action
of individual air molecules or (2) the large scale action of a large
number of molecules.
The small scale action is described by the
kinetic theory of gases and we have no evidence that the Wright
brothers were familiar with this theory when they designed the aircraft
engine. So we will not discuss the details of this theory at this web site;
if
you wish to explore the kinetic theory of gases you should visit:
http://www.grc.nasa.gov/WWW/K-12/airplane/kinth.html.
The most important result from the small scale view of temperature is that the
temperature of a gas is related to the average kinetic energy of the
moving gas molecules.
Kinetic energy is mass times the velocity squared.
So the higher the temperature of a gas,
the higher the velocity of the molecules of the gas; heating a gas causes the
molecules to move at a higher velocity. The
pressure of a gas depends on the momentum
(mass times velocity) of the molecules, so temperature and pressure are related
through an
equation of state.
Considering the large scale effects,
the temperature of a gas is something
that we can determine qualitatively with our senses. We can sense
that one gas is hotter than another gas and therefore has a higher
temperature. But to determine the temperature quantitatively,
to assign a number, we must use some principles from
thermodynamics:
- The first principle is the observation that the temperature of
an object can affect some properties of the object, such as the
length of a solid, or the gas pressure in a closed vessel, or the
electrical resistance of a wire. (Changing the temperature changes the
length of a solid bar.)
- The second principle is the definition of thermodynamic
equilibrium between two objects. Two objects are in thermodynamic
equilibrium when they have the same temperature.
- And the final principle is the observation that if two objects
of different temperatures are brought into contact with one
another, they will eventually establish a thermodynamic
equilibrium. (The word "eventually" is important. Insulating
materials reach equilibrium after a very long time, while
conducting materials reach equilibrium very quickly.)
With these three thermodynamic principles, we can construct a
device for measuring temperature, a thermometer, which assigns
a number to the temperature of an object. When the thermometer is
brought into contact with another object, it quickly establishes a
thermodynamic equilibrium. As the temperature is changed, the thermodynamic
effect is changed (the length of the mercury in the tube changes).
By measuring the thermodynamic effect on
the properties of the thermometer at some reference conditions (like the
boiling point and freezing point of water) we can establish a scale
for assigning temperature values.
The number assigned to the temperature depends on what we pick for the reference condition.
So several different temperature scales have arisen. The Celsius scale, designated with
a C, uses the freezing point of pure water as the zero point and the boiling point
as 100 degrees with a linear scale in between these extremes. The Farenheit scale, designated
with an F, is a lot more confusing. It originally used the freezing point of sea
water as the zero point and the freezing point of pure water as 30 degrees, which made the
temperature of a healthy person equal to 96 degrees. On this scale, the boiling point of pure
water was 212 degrees. So he adjusted the scale to make the boiling point of pure water 212
and the freezing point of pure water 32, which gave 180 degrees between the two reference points.
180 degrees was chosen (as it is for a circle) because it is evenly divisible by 2, 3, 4, 5, and 6.
On the new temperature scale, the heat of a healthy person is 98.6 degrees F. Because there are
100 degrees C and 180 degrees F between the same reference conditions:
1 degree C = 1 degree F * 100 / 180 = 1 degree F * 5 / 9
Since the scales start at different zero points, we can convert from the temperture on the
Farenheit scale (TF) to the temperature on the Celsius scale (TC) by using this equation:
TF = 32 + (9 / 5) * TC
Of course, you can have temperatures below the freezing point of water and these are assigned
negative numbers. When scientists began to study the coldest possible temperature, they determined
an absolute zero at which molecular kinetic energy is a minimum (but not strictly zero!).
They found this value to be at -273.16 degrees C. Using this point as the new zero point we
can define another temperature scale called the absolute temperature. If we keep the
the size of a single degree to be the same as the Celsius scale, we get a temperature scale
which has been named after Lord Kelvin and designated with a K. Then:
K = C + 273.16
There is a similar absolute temperature corresponding to the Farenheit degree. It is named after
the scientist Rankine and designated with an R.
R = F + 459.69
Absolute temperatures are used in the
equation of state
and the derivation of the state variables
enthalpy, and
entropy
which are used to solve gas dynamics problems.
Temperature, like pressure, is a scalar quantity; it has no direction
associated with it. It has just a single value at every location in a gas. The
value can change from location to location, but there is no direction connected to
the temperature.
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