Thermodynamics
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From the Greek thermos meaning heat and dynamis
meaning power is a branch of physics that studies the
effects of changes in temperature, pressure, and
volume on physical systems at the macroscopic scale
by analyzing the collective motion of their particles
using statistics.
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„
Temperature, pressure, and volume quantitatively define the
state of a gas
Temperature, pressure, and volume are state variables
We want to determine the relationship (i.e., find some
equations) between these state variables and more
importantly, relationships between changes in these
state variables.
Wikipedia: http://en.wikipedia.org/wiki/Thermodynamics
Gas Laws
1662 – Boyle’s Law
For a given constant temperature
P∝
1
V
That is, for a given constant temperature, pressure and
volume are inversely related. As one is increased, the
other must decrease. Or,
PV = constant
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Gas Laws
1787 – Charles’s Law
For a given constant pressure
V ∝T
That is, for a given constant pressure, temperature and volume are
directly related. As one is increased, the other must increase. Or,
V
= constant
T
Does not make sense using Celsius
(or Fahrenheit) scales. Need to define
a new scale called Kelvin
T (K ) = T (°C ) + 273.15
T (°C ) = T (K ) − 273.15
Note, the law is only approximate for a dilute gas and
“breaks down” near the liquefaction point.
Gas Laws
1802 – Gay Lussac’s Law
For a given constant volume
P ∝T
That is, for a given constant volume, pressure and temperature are
directly related. As one is increased, the other must increase. Or,
P
= constant
T
Note, again the law is only approximate for a dilute
gas and “breaks down” near the liquefaction point.
Also, what happens as T goes to absolute zero?
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Ideal Gas Law
Combine Boyle’s, Charles’s and Gay Lussac’s Laws
PV ∝ T
But we need to consider the amount of gas present. For a given
constant volume and temperature, the pressure is directly related to
the total mass (m) of the gas . Or,
PV ∝ mT
Or
PV = CmT
Where C is a constant of proportionality and is different for different gases.
Instead of mass, if we use the either the total number of molecules or the
number of moles, the constant of proportionality is the same for all gasses.
A mole is defined as the amount of substance that contains the same
number of atoms or molecules as there are in 12.00 g of Carbon 12.
Ideal Gas Law
Using moles
Using molecules
PV = nRT
PV = NkT
n = number of moles
N = number of molecules
R = universal gas constant
k = Boltzmann’s constant
= 8.315 J / (mol-K)
= 1.38 x 10-23 J / K
This is called the Equation of State. Why “Ideal”?
•Dilute, Volume of Molecules is ~ Zero
•No Attractions Between Molecules
•Temperature must be in Absolute Units, K
“Real” gages do not follow the ideal gas law precisely. However, at low
pressure and temperatures “not too close” to the liquefaction point, the
ideal gas law is quite accurate and useful for “real” gases.
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In an experiment, a vacuum of 1.00 x 10-10 atm is achieved in a bottle. If
the bottle is at room temperature (30.0°C), what is the number of
molecules in the bottle per cubic centimeter?
At altitudes above 14,000 ft, pilots must breathe air with enriched
oxygen because the density of the atmosphere is decreased. The
pressure of air is only about 0.26 atm at a typical height for flying of
32,000 ft. If the airplane is not pressurized, what must the fraction of
oxygen in the air be in order for a pilot to breathe the same amount of
oxygen as at sea level? Assume the temperatures to be the same and,
at sea level, 20% of the air molecules are oxygen.
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