1. The combined gas law P1 V1 P2 V2 = T1 T2 Units:
____________ ____________ =
T1 T2
Units:
P  any unit provided they match
V  any unit provided they match
T  must be in Kelvin

2. Ideal gas law PV = nRT P = absolute pressure V = volume n = # of mols
R = universal gas constant
T = absolute temperature

3. units: T must be in Kelvin Pressure Volume R Pa m3 8.31 J/mol·K
n = m/M
where: m = mass in grams and M = molar mass in g/mol

4. First Law of Thermodynamics
U = Q + W
Where :
 U  change in internal energy
Q  heat added or removed
W  work done

5. sign notation:
W  positive if work is done on the gas negative if work is done by the gas
Q  positive if heat is added negative if heat is removed
 U  positive if temperature increases negative if temperature decreases

6. where ( T = Tf - Ti ) in all cases
EQUATIONS
W = - ∫P  V where ( V = Vf - Vi )
Q = n cp  T - if pressure is constant or
Q = n cv  T - if volume is constant
 U = 3/2 nR T
where ( T = Tf - Ti ) in all cases

7. CONSTANTS cp = 5/2 R ( 20.775 J/K ) cv = 3/2 R ( 12.465 J/K )
R = 8.31 J/mol·K

8. UNITS  U  JOULES W  JOULES Q  JOULES
Therefore: Pressure must be in Pa
Volume must be in m3
R is 8.31 J/molK

9. The temperature of 3 kg of the monatomic gas krypton is raised from -20oC to 80oC. If this is done at constant volume, compute the heat added, the work done, and the change in internal energy. The molecular weight of Kr is 83.7 g/mol.
3.0 kg
1000 g
1 mol x x =
35.84 mols = n
1 kg
83.7 g
 T = 80 – -20 = 100 C° = 100K
 U = 3/2 nR T = 3/2 (35.84)(8.31)(100) =
44,700 J
Q = n cv  T = (35.84)(12.47)(100) =
44,700 J
U = Q + W ▬►
44,700 = 44,700 + W W =
0 J*
* W could have also been determined by W = -∫PV (since V = 0, W = 0)

10. Repeat the previous problem if the heating process were at constant pressure instead of constant volume.
T and the number of mols are still the same, thus U is
still the same U =
44,700 J
NOW: Q = n cp  T = (35.84)(20.78)(100) =
74,480 J
U = Q + W ▬►
44,700 = 74,480 + W W = J
Work is done by the gas since it is negative