air is a gas

8/12/2019 Air is a gas

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Air is a gas.Gases have various propertiesthat we can observe with our

senses, including the gas pressure (p),temperature (T),mass (m), and volume (V)that contains the gas. Careful, scientific observation has determined that these

variables are related to one another, and the values of these properties determine

the stateof the gas.

If we fi an! two of the properties we can determine the nature of the

relationship between the other two. If the pressure and temperature are held

constant, the volume of the gas depends directl! on the mass, or amount of gas.

This allows us to define a single additional propert! called the gas densit! (r),

which is the ratio of mass to volume. If the mass and temperature are heldconstant, the product of the pressure and volume are observed to be nearl!

constant for a real gas. (The product of pressure and volume is eactl! a constant

for an ideal gas.) This relationship between pressure and volume is called"o!le#s

$awin honor of %obert "o!le who first observed it in &''. inall!, if the mass and

pressure are held constant, the volume is directl! proportional to the temperature

for an ideal gas. This relationship is called Charles and Ga!*$ussac#s $aw in honor

of the two rench scientists who discovered the relationship.
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The gas laws of "o!le and Charles and Ga!*$ussac can be combined into a

single e+uation of state given in red at the center of the slide

p - V T / n - %

where - denotes multiplication and denotes division. To account for the effects

of mass, we have defined the constant to contain two parts a universal constant

(%) and the mass of the gas epressed in moles (n). 0erforming a little algebra, we

obtain the more familiar form

p * V = n * R * T

A three dimensional graph of this e+uation is shown at the beggining of the

net page. The intersection point of an! two lines on the graph gives a uni+ue state

for the gas.

Aerod!namicists use a slightl! different form of the e+uation of state that

is speciali1ed for air. If we divide both sides of the general e+uation b! the mass

of the gas, the volume becomes the specific volume,which is the inverse of the gas

densit!. 2e also define a new gas constant (%), which is e+ual to the universal gas

constant divided b! the mass per mole of the gas. The value of the new constant

depends on the t!pe of gas as opposed to the universal gas constant, which is the

same for all gases. The value of the e+uation of state for air is given on the slide

as .34' 5ilo 6oule per 5ilogram per degree 7elvin. The e+uation of state can bewritten in terms of the specific volume or in terms of the air densit! as

p - v / % - T or p / r - % - T

8otice that the e+uation of state given here applies onl! to an ideal gas, or a

real gas that behaves li5e an ideal gas. There are in fact man! different forms for

the e+uation of state for different gases. Also be aware that the temperature

given in the e+uation of state must be an absolute temperaturethat begins at

absolute 1ero. In the metric s!stem of units, we must specif! the temperature in

degrees 7elvin (not Celsius). In the 9nglish s!stem, absolute temperature is indegrees %an5ine (not ahrenheit).
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'

Air is a gas.Gases have various propertieswhich we can observe with oursenses, including the gas pressure (p),temperature,mass, and the volume (V) which

contains the gas. Careful, scientific observation has determined that these

variables are related to one another, and the values of these properties determine

the stateof the gas.

In the mid &'#s, %obert "o!le studied the relationship between the

pressure and the volume of a confined gas held at a constant temperature. "o!le

observed that the product of the pressure and volume are observed to be nearl!

constant. (The product of pressure and volume is eactl! a constant for an idealgas.) This relationship between pressure and volume is called Boyle's Law in his

honor. or eample, suppose we have a theoretical gas confined in a :ar with a

piston at the top. The initial state of the gas has a volume e+ual to ;. cubic

meters and the pressure is &. 5ilopascal. 2ith the temperature and number of

moles held constant, weights are slowl! added to the top of the piston to increase

the pressure. 2hen the pressure is &.


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cubic meters. The product of pressure and volume remains a constant (; &. / <

&.


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temperatures.) As the gas cools, the volume decreases to

air is a gas

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