Useful Constants
gravitational acceleration g=9.8m/s,
gas constant R=8.31446 Jmol-1 K-1,
Boltzman constant k=1.38064x10-23JK-1,
Avogadro number NA=6.02214x1023,
8
speed of light c=3x10 m/s,
1 atmospheric pressure=1.01325x105 Pa,
Useful Calculus equations
𝑑 𝑓(𝑎𝑡)
𝑑
𝑑𝑡
=𝑎
𝑑𝑓(𝑥)
𝑑𝑥
𝑑
𝑑
𝑎𝑡 𝑛 = 𝑎𝑛𝑡 𝑛−1 , 𝑑𝑡 sin 𝑎𝑡 = a cos 𝑎𝑡,
𝑑𝑡
with 𝑥 = 𝑎𝑡,
cos 𝑎𝑡 = −𝑎 sin 𝑎𝑡
𝑑𝑡
Useful Equations
,
, C = ABsin f ,
,
,
Temperature scale: T = 9/5 T + 32°, T = 5/9 (T – 32°), T = T + 273.15
F
C
C
F
K
C
Thermal expansion: L   L0 T , V   V0 T ,   3
Heat: Q  mc T , Q   mL
;
Heat conduction: H = dQ/dt = kA(TH– TC)/L
4
Stefan-Boltzmann law: H  Ae T
Ideal gas:
pV = nRT , r =
mtotal pM
=
, mtotal = nM ,
V
RT
Molecular Kinetics: K tr 
3
nRT ,
2
p1V1 p2V2
=
T1
T2
1
3
m  v 2   kT ,
av
2
2
k
R
NA
Molar heat capacity: dQ  nCdT ,
mean free path: l =
5
3
CV = R (monatomic ) , CV = R (diatomic )
2
2
,
V
4p 2r 2 N
Waves:
2
2
I
r2
   f , k  2 /  ,   vk ,  y2  12  2y , y(x,t) = Acos(kx – t) , 1  22
x
F
String: v 
fn  n

2L
Sound:
B
v
I

, Pmax   F2 A2 ,

 n  1, 2, 3,...
 nf1
(fluid), v 
Y

v t
Pav 
r1
1
 F  2 A2
2
(string fixed at both ends)
(solid rod),
p 2
1
 B 2 A2  max ,
2
2
I2
v
 RT
M
(ideal gas, 𝛾 = 1.4)
pmax  BkA
 = (10 dB) log(I/I0)
 = 2L/n and f = nv/2L (n = 1, 2, 3, …) (open pipe)
n
n
 = 4L/n and f = nv/4L (n = 1, 3, 5, …) (pipe where one end is open and the other
n
n
end is closed)
fbeat= fa – fb (beating)
fL =
,
u ± uL
f (Doppler effect)
u ± uS S
(Doppler effect)
Light:
n = c/v,
sin crit 

nb
na
0
n
,  r  a
law of reflection na sin a  nb sin b  law of refraction
 critical angle for total internal reflection 
nb
 Brewster's angle 
na
I = Imaxcos2 (Malus's law)
tan  p 
-End of equation list-