Exam equation sheet from previous semesters

2
0 K = −273.15◦ C 0◦ C = 32◦ F 4.186 J = 1 cal σ = 5.67 × 10−8 W/m K4 1.00 atm = 1.013 × 105 Pa = 14.7 psi
R = 8.314 J/(mol · K) kB = 1.38 × 10−23 J/K c = 4186 J/(kg ·◦ C) (Specific heat of liquid water) 1 m3 = 1000 L
c = 3.00 × 108 m/s 1 eV = 1.60 × 10−19 J c = 1996 J/(kg ·◦ C) (Specific heat of water vapor)
me = 9.11 × 10−31 kg mp = 1.67 × 10−27 kg c = 2108 J/(kg ·◦ C) (Specific heat of water ice)
c = 450 J/(kg ·◦ C) (Specific heat of iron) L = 3.33 × 105 J/kg (Latent heat of fusion for water ice)
3
L = 2.26 × 106 J/kg (Latent heat of vaporization for water vapor) ρwater = 1000 kg/m
W = nRT ln
Vi
Vf
(isothermal)
P =
∆Q
= kA
∆t
Th − Tc
L
Nv = 4πN
m
2πkB T
3/2
v 2 e−mv
2
/2kB T
1
P + ρv 2 +ρgh = constant ∆L = αLi ∆T ∆V = βVi ∆T β = 3α A1 v1 = A2 v2 = constant
2
4 3
2
Asphere = 4πr Vsphere = πr P V = N kB T = nRT − Qhot = Qcold Q = mc∆T Q = L∆m dW = −P dV
3
3
3
∆Q
= σAeT 4 Ktot trans = N kB T = nRT Q = nCV ∆T Q = nCP ∆T CP = CV +R γ = CP /CV
∆Eint = Q+W P =
∆t
2
2
r
r
r
C
Vf
1
3k
8kB T
2kB T
P
BT
γ
vrms =
vavg =
vmp =
∆S = nR ln
CV = R·(#d.o.g.) P V = constant γ =
2
CV
m
πm
m
Vi
P = ρgh
B = ρfluid gVdisp
e≡
Weng
|Qh |
Weng = |Qh | − |Qc |
n
n!
=
k
k!(n − k)!
fn = n
v
2L
f (x) = b0 +
P =
S ≡ kB ln W
1 2 2
µω A v
2
fn = n
∞
X
Tc
(Carnot engine efficiency)
Th
eC = 1 −
bn cos
n=1
v
4L
2πnx
L
+
∞
X
2
L
I
I0
L
Z
f (x) sin
0
an sin
n=1
2πnx
L
n2
n2 − n1
n1
+
=
p
q
R
1
= (n − 1)
f
sin x
x
I = I0 sinc2
πa
λ
2d sin θbright = mλ (Bragg)
1
γ=p
1 − β2
u0x
v
β=
c
ux − v
=
1 − ucx2v
s
0
f =f
1±β
1±β
Etot = K + ER
sin θ
1
1
−
R1
R2
2
I ∼ |E|
dx
n=
Z
c
v
M=
L
m=
λ
a
θ
θ0
f (x)dx
0
∆t2 = γ∆t1
λ
D
dQr
T
f (x) cos
0
πd
sin θ
λ
vgroup
2πnx
L
dx
1
2nt = (m + )λ
2
P =
R = Nm =
x0 = γ(x − vt)
ER = mc2
Aˆ
p exp{iφ} exp{i(~k · ~r − ωt)}
1 1
1
+ =
p q
f
L
I = Imax cos2 θ
L2 = L1 /γ
K = (γ − 1)mc2
Z
2nt = mλ
I = I0 cos2
θmin = 1.22
h0
−q
=
h
p
2
bn =
L
d sin θbright = mλ
v t0 = γ t − 2 x
c
f
dS =
sin θ = 1/mach#
f2 /f1 = 21/12
s
r
T
n
T
2L
fn =
v(T ) = 331 1 +
λn =
n
2L µ
273 ◦ C
1
b0 =
L
sin θdark = m
n = tan θp
v ± v0
v ± vs
2πnx
L
θBrewster = tan−1 (n2 /n1 )
f0 =
n1 sin θ1 = n2 sin θ2
sinc x =
1
(Otto cycle)
(V1 /V2 )γ−1
f (x, t) = A sin(kx − ωt + φ)
β = 10 log
an =
e=1−
λave
λ
p = γmv
E 2 = p2 c2 + (mc2 )2
∂ω =
∂k k=k¯
F
A
E = pc
ω
¯
vphase = ¯
k
eiθ + e−iθ
eiθ − e−iθ
x2
x4
x3
x5
sin θ =
cos x = 1 −
+
− · · · sin = x −
+
− ···
2
2i
2!
4!
3!
5!
x
x2
x3
n(n − 1) n−2 2
ex = 1 + +
+
+ ···
(a + x)n = an + nan−1 x +
a
x + · · · + xn
1!
!2
3!
2
eiθ = cos θ + i sin θ
cos θ =
1

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