2nd Midterm 2012
Chapter 37
HELP SHEET
Interference of Light Wave
Two Slits Separated by a distance d
Path Difference (Constructive Interference):
 = dsinb = m
Path Difference (Destructive Interference):
 = dsind = (m +½)
For small :
sin  tan = y/L
Position of a Bright Fringe:
yb = mL/d
Position of a Dark Fringe:
yd = (m +½) L/d
(m = 0, ±1, ±2…)
(m = 0, ±1, ±2…)
( m = 0, ±1, ±2…)
(m = 0, ±1, ±2…)

Phase Difference (Constructive Interference):
2

d sin 
Average Light Intensity (Constructive Interference): I av  I max cos2     I max cos2  2 d sin    I max cos2  d y 
 
2
Chapter 19

 L 
Temperature
Conversions: TC  TK  273
TK  TC  273
TF 
9
TC  32
5
TC 
5
TF  32 
9
Equation of State for an Ideal Gas: PV = nRT
Universal Gas Constant: R = 8.314 J/mol K
R = 0.08206 atm-L/mol K
Conversion Units: (Pascal) 1Pa = N/m2 = 1J/m3
1J = Pa-m3
Chapter 20
1atm = 1.01x105Pa
1atm-L = 101J
Heat and the First Law of Thermodynamics
Heat: Q  Amount of Transfer of Energy
Mechanical Equivalent of Heat: 1 cal = 4.186 J
Heat Capacity: C = Q/T
Where: (T = Tf – Ti)
Specific Heat: c = Q/mT
Conservation of the Energy:
Qcold  Qhot
Transfer Energy: Q = cmT
Change Phase Energy Transfer: Q = ± mLv,f
(T remains constant, so T = 0)
Work done ON a Gas (Volume changes): W  
1st Law of Thermodynamics:
Eint = Q + W

Vf
Vi
PdV  ̶ (Area under the PV diagram)
Q = Energy transferred into the gas by heat.
W = Work done on the gas
SPECIAL PROCESSES:
Isolated system: Q = W = 0, so Eint = 0
Adiabatic Free Expansion: Q = W = 0, so Eint = 0
Adiabatic Process: Q = 0, so Eint = W
Isobaric (Constant pressure): W = P (Vf – Vi), so Eint = Q + W
Isothermal (Constant temperature): Eint = 0, so Q = –W
Isovolumetric (Constant Volume): W = 0, so Eint = Q
Cyclic Process: Eint = 0, so Q = –W
Isothermal Expansion: W = (nRT)ln(Vi/Vf)
Chapter 21
The Kinetic Theory of Gases
Pressure of N Particles (Ideal Gas): P 
2
3
N
V

1
2
mv 2 
Average Translational Kinetic Energy per molecule:
Root-Mean-Square Speed: vrms  v 2 
1
2
mv 2  23 k BT or
3kBT
m
1
2
2
mv rms
 32 k B T
Boltzmann’s Constant:
kB 
R
 1.4  10  23 J / K
NA
Monatomic Gas (Ideal Gas):
Internal Energy (N molecules or n mole): Eint =3/2(NkBT) = 3/2(nRT)
Change in Internal Energy: Eint = nCVT
Molar Specific Heat (Volume Constant): CV = (3/2)R
Molar Specific Heat (Pressure Constant): CP = (5/2)R
Ratio of Specific Heats:  = CP / CV =5/3
Adiabatic Expansion or Compression: PV  = Constant
P V
i i

 P f V f

or
PT  -1 = Constant
P T
i i
 1
 P f V f 1
