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PHY 317K
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Some Equations for Final Exam
• Temperature conversions for T in Kelvin: TC = T − 273.15◦ and TF = 59 TC + 32◦ .
• Conductive heat flow for a material with thermal conductivity k: H = −kA
• Heat capacity C =
∆T
.
∆x
Q
C
Q
C
Q
; specific heat c =
=
; molar specific heat c =
=
.
∆T
m
m∆T
n
n∆T
• Thermal expansion of solids: if α is the coefficient of linear expansion, ∆L = αL∆T .
• Phase changes: for solid ↔ liquid, Q = mLF , for liquid ↔ gas, Q = mLV .
• Boltzmann constant: k = 1.38 × 10−23 J/K; Avogadro constant: NA = 6.02 × 1023 mol−1
gas constant: R = kNA = 8.31 J/mol·K; molar mass: M = NA m, if m is the mass of one
molecule.
• First Law of Thermodynamics: ∆Eint = Q + W , where Q is the heat into the system and W
is the work done on the system. For a closed system, ∆Eint = 0.
• For an ideal gas: pV = nRT = N kT , where n = N/NA and N is the number of molecules.
• Work by a gas: W =
• Isothermal process:
Isobaric process:
Isochoric process:
Adiabatic process:
Z Vf
p dV .
Vi
T = const;
p = const;
V = const;
Q = 0;
pV γ = const,
W = −nRT ln( VV21 ),
W = −p(V2 − V1 ),
W = 0,
2 −p1 V1
W = p2 Vγ−1
,
where γ = Cp /CV
Q = −W ,
Q = ∆Eint − W ,
Q = ∆Eint ,
∆Eint = W ,
T V γ−1 = const,
pV = const
Q = nCp ∆T
Q = nCV ∆T
and
• Internal energy: Eint = f2 nRT , where f is the number of degrees of freedom.
Molar specific heat: CV = f2 R, and Cp = CV + R.
• For a monatomic ideal gas: vrms =
p
(v 2 )ave =
q
3p
ρ
=
q
3RT
M
=
q
3kT
m .
• Second Law of Thermodynamics: for a closed system, ∆S ≥ 0, where entropy change is given
Z f
Z b
dQ
dx
b
by ∆S =
.
Recall:
= ln( ).
T
x
a
i
a
work performed
W
=
;
heat used
|Qh |
Tc
Qc
for a Carnot engine: e = 1 −
=1−
.
Th
Qh
• Efficiency of a heat engine: e =
1