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Heat expansion
Δ
L
L
=
α
Δ
T
\frac{\Delta L}{L}=\alpha\Delta T
L
Δ
L
=
α
Δ
T
Δ
V
V
=
β
Δ
T
\frac{\Delta V}{V}=\beta\Delta T
V
Δ
V
=
β
Δ
T
β
=
3
α
\beta=3\alpha
β
=
3
α
Heat
Q
=
m
c
Δ
T
Q=mc\Delta T
Q
=
m
c
Δ
T
l
s
=
Q
s
m
l_s=\frac{Q_s}{m}
l
s
=
m
Q
s
l
a
=
Q
a
m
l_a=\frac{Q_a}{m}
l
a
=
m
Q
a
%a ska egentligen vara å
Fluid preassure
p
t
o
t
=
p
fluid
+
p
air
=
ρ
g
h
+
p
air
p_{tot} = p_\textup{fluid} + p_\textup{air} = \rho gh + p_\textup{air}
p
t
o
t
=
p
fluid
+
p
air
=
ρ
g
h
+
p
air
%funkar det att skirva ä eller måste det vara så här?
Ideal gas law
p
V
=
N
k
T
pV=NkT
p
V
=
N
k
T
p
V
=
n
R
T
pV=nRT
p
V
=
n
RT
Gas density and particle density
ρ
=
m
t
o
t
V
=
p
M
R
T
,
n
o
=
N
V
=
p
k
T
\rho = \frac{m_{tot}}{V} = \frac{pM}{RT}, \quad n_o = \frac{N}{V} = \frac{p}{kT}
ρ
=
V
m
t
o
t
=
RT
pM
,
n
o
=
V
N
=
k
T
p
Barometric height formula
p
=
p
0
e
−
ρ
0
g
h
/
p
0
,
h
=
p
0
ρ
0
g
ln
p
0
p
p = p_0e^{-\rho_0gh/p_0}, \quad h = \frac{p_0}{\rho_0g}\ln{\frac{p_0}{p}}
p
=
p
0
e
−
ρ
0
g
h
/
p
0
,
h
=
ρ
0
g
p
0
ln
p
p
0
Relative humidity
R
M
=
p
water
p
saturation
R_{M} = \frac{p_\textup{water}}{p_\textup{saturation}}
R
M
=
p
saturation
p
water
van der Waals' equation
(
p
+
a
n
2
V
2
)
(
V
−
n
b
)
=
n
R
T
\left(p + a\frac{n^2}{V^2}\right)(V - nb) = nRT
(
p
+
a
V
2
n
2
)
(
V
−
nb
)
=
n
RT
Critical point
V
k
=
3
n
b
,
T
k
=
8
a
27
R
b
,
p
k
=
a
27
b
2
V_k = 3nb, \quad T_k = \frac{8a}{27Rb}, \quad p_k = \frac{a}{27b^2}
V
k
=
3
nb
,
T
k
=
27
R
b
8
a
,
p
k
=
27
b
2
a