1. Temperature and Ideal Gas
PHYSICS 220
Lecture 22
Temperature and Ideal Gas
Lecture 22
Purdue University, Physics 220

2. Molecular Picture of Gas
Gas is made up of many individual molecules
Number of moles n = N / NA
NA = Avogadro’s number = 6.0221023 mole-1
NA= number of particles (can be atoms or molecules) per mole
1 mole = amount of substance that contains as many elementary entities as there are atoms in exactly 12 grams of carbon-12
Lecture 22
Purdue University, Physics 220

3. Atoms, Molecules and Moles
1 mole =  1023 molecules (NA = Avogadro’s Number)
NA = Number of atoms or molecules that make a mass equal to the substance's atomic or molecular weight in grams.
1 u = 1 atomic mass unit = (mass of 12C atom)/12
Approximately # of neutrons + # of protons
Atomic weight A
1 u = 1.66  kg = 1gram/NA
Mass of 1 mole of “stuff” in grams = molecular mass in u
E.g. 1 mole of N2 has mass of 2  14 = 28 grams
Lecture 22
Purdue University, Physics 220

4. Purdue University, Physics 220
iClicker
Which contains more molecules ?
A) A mole of water (H2O)
B) A mole of oxygen gas (O2)
C) Same
H2O O2
Lecture 22
Purdue University, Physics 220

5. Purdue University, Physics 220
Question
Which contains more atoms ?
B) A mole of water (H2O)
C) A mole of oxygen gas (O2)
A) Same
H2O (3 atoms)
O2 (2 atoms)
Lecture 22
Purdue University, Physics 220

6. Purdue University, Physics 220
Question
Which weighs more ?
A) A mole of water (H2O)
B) A mole of oxygen gas (O2)
C) Same
H2O (M = )
O2 (M = )
Lecture 22
Purdue University, Physics 220

7. Internal Energy
All objects have “internal energy” (measured in Joules)
random motion of molecules +energy associated with intermolecular bonds
kinetic energy potential energy
collisions of molecules gives rise to pressure
Amount of internal energy depends on
temperature
related to average kinetic energy per molecule
how many molecules
mass
“specific heat”
related to how many different ways a molecule can move
Translation (the only one for monatomic gas)
Rotation
vibration
the more ways it can move, the higher the specific heat

8. Temperature
Feel
Measure

9. Zeroth Law of Thermodynamics
If two (or more) objects are in thermal equilibrium, they are at the same temperature.
If two objects are in thermal equilibrium with a third, then the two are in equilibrium with each other.
Perhaps do hot water, and cold, comment on what happens after time.

10. Temperature Scales Anders Celsius (1701 - 1744) Daniel G. Fahrenheit
( )
Lord Kelvin
( )

11. Temperature Scales Farenheit Celcius Kelvin 100 373.15 212 Water boils32
Farenheit
100
Celcius
273.15
373.15
Kelvin
Water boils
Water freezes
NOTE: K=0 is “absolute zero”, meaning (almost) zero KE/molecule

12. iClicker K = C + 273 A) One B) Two C) Same
Two cups of coffee are heated to 100 degrees Fahrenheit. Cup 1 is then heated an additional 20 degrees Centigrade, cup 2 is heated an additional 20 Kelvin. Which cup of coffee is hotter?
A) One B) Two C) Same
K = C + 273

13. Purdue University, Physics 220
Gay-Lussac’s Law
If const V: P  T
Inventor of the hydrogen balloon
Lecture 24
Purdue University, Physics 220

14. Purdue University, Physics 220
Other Empirical Laws
Charles’s law
If const P: V  T V  T
Boyle’s Law
Avogadro’s Law
If const T: P  1/V
If const P and T: V  N
Lecture 24
Purdue University, Physics 220

15. Purdue University, Physics 220
The Ideal Gas Law
P V = N kB T
P = pressure in N/m2 (or Pascals)
V = volume in m3
N = number of molecules
T = absolute temperature in K
k B = Boltzmann’s constant = 1.38 x J/K
Note: P V has units of N*m or J (energy!)
Lecture 24
Purdue University, Physics 220

16. Purdue University, Physics 220
The Ideal Gas Law
PV = NkBT
Alternate way to write this
N = number of moles (n) x NA molecules/mole
PV= NkBT
nNAkB T
n(NAkB)T
nRT
P V = n R T
n = number of moles
R = ideal gas constant = NAkB = 8.31 J/mol/K
Lecture 24
Purdue University, Physics 220

17. Purdue University, Physics 220
Exercise
You inflate the tires of your car so the pressure is 30 psi, when the air inside the tires is at 20 degrees C. After driving on the highway for a while, the air inside the tires heats up to 38 C. Which number is closest to the new air pressure?
A) 16 psi B) 32 psi C) 57 psi
Careful, you need to use the temperature in K
P = P0 (38+273)/(20+273)
Lecture 24
Purdue University, Physics 220

18. Purdue University, Physics 220
Question
What happens to the pressure of the air inside a hot-air balloon when the air is heated? (Assume V is constant)
A) Increases B) Same C) Decreases
Balloon is still open to atmospheric pressure, so it stays at 1 atm
Lecture 24
Purdue University, Physics 220

19. Purdue University, Physics 220
Question
What happens to the buoyant force on the balloon when the air is heated? (Assume V remains constant)
A) Increases B) Same C) Decreases
FB = r V g
r is density of outside air!
Lecture 24
Purdue University, Physics 220

20. Purdue University, Physics 220
Question
What happens to the number of air molecules inside the balloon when the air is heated? (Assume V remains constant)
A) Increases B) Same C) Decreases
PV = NkBT
P and V are constant. If T increases N decreases.
Lecture 24
Purdue University, Physics 220

21. Purdue University, Physics 220
Balloon
In terms of the ideal gas law, explain briefly how a hot air balloon works.
Once the air in a balloon gets hot enough, the net weight of the balloon plus this hot air is less than the weight of an equivalent volume of cold air, and the balloon starts to rise.
When temperature increases the volume of the gas increases, thus reducing the density of the gas making it lighter that then surrounding air, which causes the balloon to rise.
Note! this is not a pressure effect, it is a density effect. As T increases, the density decreases the balloon then floats due to Archimedes principle. The pressure remains constant!
Lecture 24
Purdue University, Physics 220