Gas Laws
Gas Laws
p – absolute pressure
For a given constant pressure
Volume
Temperature
An air piston has a volume of 0.3 ft3 pressure 0 psig. The
piston slowly compresses the air (temperature = constant) to
a volume of 0.15 ft3. What is the final pressure?
(patm = 14.7 psi).
EF 152 Spring, 2010 Lecture 3-3
Volume
For a given constant temperature
1787 – Charles’s Law
Pressure
1662 – Boyle’s Law
An air piston has a volume of 0.5 m3 and a temperature of
20°C. The temperature is increased to 40°C under constant
pressure. What is the final volume?
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EF 152 Spring, 2010 Lecture 3-3
Ideal Gas Law
1802 – Gay-Lussac’s Law
Combine Boyle’s, Charles’s and Gay Lussac’s Laws
For a given constant volume
Pressure
Gas Laws
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Also need to incorporate the amount of gas present, or
the mass.
Temperature
Tires are filled to a pressure of 200 kPa(g) (29 psig) at 10°C.
After a drive of 100 km, the temperature in the tires is 40°C
(constant volume). Assume a constant volume. What is the
final pressure in the tires? (patm = 101 kPa).
•  The proportionality constant, C, varies for different gases.
•  The proportionality constant is the same for all gases if
we express the amount of gas in terms of moles instead
of in mass.
EF 152 Spring, 2010 Lecture 3-3
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EF 152 Spring, 2010 Lecture 3-3
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Ideal Gas Law
Example: Mass of air in a room
•  Mole (mol): amount of substance that contains as many
atoms or molecules that are in precisely 12 grams of
carbon 12.
A room measures 30 m x 30 m by 8 m and contains air at
20°C (68°F). What is the mass of air in the room?
•  Quantity of substance whose mass in grams is
numerically equal to the molecular mass.
1.  Order of magnitude guesstimate.
2.  Ideal gas law estimate.
•  Molecular mass given in Periodic Table.
n = number of moles; mass in
grams / molecular mass
R = universal gas constant
= 8.314 J / (mol-K)
Air is about 20% oxygen (O2) and 80% nitrogen (N2). The molecular
masses are 2x16=32 and 2x14=28 respectively. An average value is
about 29.
Laws are only approximations. Accurate if:
•  Pressure and density not too high
•  Gas not too close to liquefaction
EF 152 Spring, 2010 Lecture 3-3
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EF 152 Spring, 2010 Lecture 3-3
Ideal Gas Law: Other Forms
Examples:
•  Avogadro’s number: number of molecules in one mole;
6.02x1023
N = number of molecules
Estimate how many molecules you breathe in with a
1 L breath of air.
k = Boltzmann constant
= 1.38x10-23 J/K
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Closed test tube: V=28 cm3 of air, p=1 atm, T=17 °C.
Stopper: diameter=2.0 cm, will pop off with net upward force of 19 N.
Find the temperature required to pop off the stopper.
•  Standard Temperature and Pressure (STP)
T = 273K p = 1.00 atm (101.3kPa)
Volume of 1 mole of any gas at STP is 22.4 L
•  van der Walls equation – a ‘better’ ideal gas law
a and b are empirical constants that are gas specific.
!
an 2 $
p
+
#
& (V ' nb) = nRT
V2 %
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EF 152 Spring, 2010 Lecture 3-3
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EF 152 Spring, 2010 Lecture 3-3
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