Some Equations for the Final Exam
•
Pressure vs depth
h
in a fluid of density
ρ
:
p
=
p
0
+
ρgh
, if
p
0
is pressure at the surface.
•
Archimedes’ Principle: The magnitude of the buoyant force on an object equals the
weight of the fluid it displaces.
•
Equation of Continuity:
ρAv
= constant
•
Bernoulli’s Equation:
p
+
1
2
ρv
2
+
ρgh
= constant
•
Temperature conversions for
T
in Kelvin:
T
C
=
T

273
.
15
◦
and
T
F
=
9
5
T
C
+ 32
◦
.
•
Thermal expansion of solids: if
α
is the coefficient of linear expansion,
Δ
L
=
αL
Δ
T
,
Δ
A
= 2
αA
Δ
T
,
and
Δ
V
= 3
αV
Δ
T
.
•
Heat capacity
C
=
Q
Δ
T
; specific heat
c
=
C
m
=
Q
m
Δ
T
; molar specific heat
c
=
C
n
=
Q
n
Δ
T
.
•
Phase changes: for solid
↔
liquid,
Q
=
mL
F
for liquid
↔
gas,
Q
=
mL
V
•
Conductive heat flow for a material with thermal conductivity
k
:
H
=

kA
Δ
T
Δ
x
.
•
Boltzmann constant:
k
= 1
.
38
×
10

23
J/K
Avogadro constant:
N
A
= 6
.
02
×
10
23
mol

1
gas constant:
R
=
kN
A
= 8
.
31 J/mol
·
K
molar mass:
M
=
N
A
m
, if
m
is the mass of one molecule.
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 Spring '07
 KOPP
 Thermodynamics, Entropy, Fundamental physics concepts, Molar Specific heat, mol−1 gas constant

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