"Thermal Physics" formula sheets

PHY 3513 Page 1
“Thermal Physics” Fall 2003
Formula and Fact Sheet (Version of 26 September 2003)
Professor Mark W. Meisel
N A = 6.0222 × 10 23 particles mol −1 1 atm = 1.01325 bar
k B = 1.3806 × 10 −23 J K −1 = R N A
1 Torr = 133.3 N m −2 = 133.3 Pa
k B = 8.617 × 10 −5 eV K −1
1 eV = 1.602 × 10 −19 J
R = 8.3143 J mol −1 K −1
1 bar = 10 5 N m −2 = 10 5 Pa
1 J = 2.39 × 10 −4 kcal 1 kcal = 4184 J
h = 6.626 × 10 −34 J s
¯h = 1.054 × 10 −34 J s
h = 4.136 × 10 −15 eV s
¯h = 6.579 × 10 −16 eV s
(T in ◦ C) = (T in K) −273.15 (T in ◦ F) = 9 (T in ◦ C) +32
5
(1 + x) n = 1 + n 1! x + n(n−1)
2!
x 2 + · · ·
x = x(y, z)
dx = ( )
∂x
dy + ( )
∂x
dz
∂y z ∂z y
P v = RT
( ) ∂x
( ) ∂y
∂y z ∂z x
(
P V = nRT
P +
a
( )
( )
β = 1 ∂V
κ = − 1 ∂V
V ∂T P
V ∂P T
dU = −d ′ W ad Q ≡ W − W ad dU =d ′ Q−d ′ W
ρ = m d ′ W = βP V dT − κP V dP d ′ W = P dV
V
C = ∆Q
∆T
c P − c V =
[( )
∂u
∂v
c P − c V = − [( ∂h
∂P
c P − c V = R
C = d′ Q
dT
+ P ] ( )
∂v
) T ∂T P
− ( )
v] ∂P
T ∂T V
c V = ( )
d ′ q
dT
c V = ( )
∂u
η ≡ ( ∂T
∂v
V
∂T)
V
u
( ) ∂z
= −1
∂x
) y
v (v − b) = RT
2
P v = A + B v + C v 2 + · · ·
c P = ( )
d ′ q
dT
c P = ( )
∂h
µ ≡ ( ∂T
∂P
P
∂T)
P
γ ≡ c P
cV
P v γ = Const. T v γ−1 = Const. ′
w = 1 [P 1−γ 2v 2 − P 1 v 1 ] w = c v (T 1 − T 2 ) q = c P (T 2 − T 1 )
h
H = U + P V h = u + P v l ≈ ∆Q
(h2 ) ( ) ∆m
+ 1 2 ν2 2 + gz 2 − h1 + 1 2 ν2 1 + gz 1 = q − wsh dH = d ′ Q P
l = h i − h j
P + 1 2 ρν2 + ρgz = Const.
u = u o + c v (T 2 − T 1 ) − a v
Q 1
Q 2
= T 1
T 2
η = W Q 2
= 1 − T 1
T 2
c = Q 1
W = T 1
T 2 −T 1
η(Otto) = 1 − Q 1
Q 2
= 1 − 1
r (γ−1)
η(Joule) = 1 − ( P a
P b
) (γ−1)/γ
r = Va
V b

PHY 3513 Page 2
“Thermal Physics” Fall 2003
Formula and Fact Sheet (Version of 17 November 2003)
Professor Mark W. Meisel
dS ≡ d′ Q r
∆s = l (∆s)
T v
= ∫ T 2
T 1
∆S ≥ 0
dU = T dS − P dV
T ds = c v dT + T ( )
∂P
dv (∆s) ∂T v P = ∫ T 2
T 1
T ds = c P dT − T ( )
∂v
( )
dP
∂T P ( )
T ds = c ∂T
∂T
P ∂v
∂P
P dv + c v
c v
dT
T
c P
dT
T
dP c P − c v = β2 T v
v κ
U
H = U + P V
F = U − ST
G = U − T S + P V
dU = T dS − P dV
dH = T dS + V dP
dF = −SdT − P dV
dG = −SdT + V dP
( ) ∂T
( ∂V ) ∂T
( = ∂P ) S
∂S
( = ∂V ) T
∂S
∂P
= − ( )
∂P
S ∂S)
( V
∂V
( ∂S ) P
∂P
∂T
T = − ( ∂V
∂T
) V
P
( ) dP
= (s s−s l )
= l s−l
dT s−l( (v)
s −v l )
lim ∂ ∆G
T →0 ∂T
T (v l −v s )
g 1 = g 2
P = 0 lim T →0
( ∂ ∆H
∂T
)
P = 0 lim T →0 S = 0
d ′ W = [ −σ dA d ′ Q T = λ dA T dU = T dS − P dV + σ dA
dU = T ( )
∂S
− P ( ) ] [
∂V
dT + T ( )
∂S
− P ( ) ] [
∂V
dP + σ + T ( )
∂S
− P ( )
∂V
∂T P,A ∂T P,A
∂P T,A ∂P T,A
∂A T,P ∂A
[
dU = [C P,A − P V β P,A ] dT + [P V κ T,A − T V β P,A ] dP + σ − T ( )
∂σ
− P ( ) ]
∂V
dA
∂T P,A ∂A T,P
dU = [ σ − T ( ) ( )]
dσ
dT − P dV
dA dA
dU = [ σ − T ( )]
dσ
dT dA
S = −A dσ
dT
P i − P e = 2σ r
E = − 4π 3 r3 (∆g) + 4π r 2 σ
s = − dσ
dT
λ = − T dσ
dT
ln p
p ◦
= v l
RT (P − p ◦) r = 2 σ v l
RT ln( p
R c = 2σ
∆g
d ′ W = −H dM dU = T dS + H dM E p = − H M
E T = U + E p dE T = T dS − M dH C H = ( )
∂E
∂T H
C M = ( )
∂U
F ∗ = E − T S
dF ∗ = − S dT − M dH
∂T M
M = χ H χ = C χ = C
T T −Θ
p◦ )
T,P
]
dA