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程序代写案例-PHYS1001
时间：2022-06-16
PHYS1001 Semester 1, 2021 Page 1 of 2
PHYS1001 Physics 1 (Regular)
Data and Formula Sheet
Data
Density of fresh water ρ = 1.00× 103 kg.m−3
Free fall acceleration at Earth’s surface g = 9.80 m.s−2
Gravitational constant G = 6.67× 10−11 N.m2.kg−2
Speed of light in a vacuum c = 3.00× 108 m.s−1
Speed of sound in air v = 344 m.s−1
Avogadro constant NA = 6.023× 1023 mol−1
Universal gas constant R = 8.314 J.mol−1.K−1
Boltzmann constant kB = 1.381× 10−23 J.K−1
Stefan-Boltzmann constant σ = 5.67× 10−8 W.m−2.K−4
Conversion of temperature scales 0◦C = 273.15 K
Oscillations
ω = 2pif =
2pi
T
, f =
ω
2pi
=
1
T
ω =
√
k
m
, ω =
√
κ
I
ω =
√
g
L
, ω =
√
mgd
I
Fx = −kx
x = A cos(ωt+ φ)
E =
1
2
mv2x +
1
2
kx2 =
1
2
kA2 = constant
x = Ae−(b/2m)t cosω′t, ω′ =
√
k
m
− b
2
4m2
bcritical = 2
√
km
A =
Fmax√(
k −mω2d
)2
+ b2ω2d
Longitudinal sound waves
v =
√
B
ρ
(fluid), v =
√
Y
ρ
(solid rod)
v =
√
γRT
M
(ideal gas)
fn =
nv
2L
(n = 1, 2, 3, . . .) (open pipe)
Mechanical waves
v = λf, k =
2pi
λ
ω = 2pif = vk, v =
√
F
µ
y(x, t) = A cos(kx± ωt)
y(x, t) = (ASW sin kx) sinωt (standing wave)
String fixed at both ends:
fn = n
v
2L
= nf1 (n = 1, 2, 3, . . .)
f1 =
1
2L
√
F
µ
β = (10 dB) log
I
I0
fn =
nv
4L
(n = 1, 3, 5, . . .) (stopped pipe)
fL =
v + vL
v + vS
fS (+ from L to S)
sinα =
v
vS
fbeat = |fa − fb|
PHYS1001 Semester 1, 2021 Page 2 of 2
Thermal physics
∆L = αL0∆T, ∆V = βV0∆T
Q = mc∆T, Q = nC∆T, Q = ±mL
pV = nRT = NkT N = nNA
CV =
3
2
R (ideal monatomic gas)
CV =
5
2
R (ideal diatomic gas)
CV = 3R (ideal monatomic solid)
CP = CV +R, γ =
CP
CV
vrms =
√
3RT
M
mtot = nM = nNAm
e =
W
QH
= 1 +
QC
QH
= 1−
∣∣∣∣QCQH
∣∣∣∣
eCarnot = 1− TC
TH
=
TH − TC
TH
KCarnot =
TC
TH − TC
eOtto = 1− 1
rγ−1
Ktr =
3
2
nRT,
1
2
m(v2)av =
3
2
kT
W =
∫ V2
V1
p dV, ∆U = Q−W
dU = dQ− dW (infinitesimal process)
K =
|QC |
|W | =
|QC |
|QH | − |QC |
∆S =
∫ 2
1
dQ
T
(reversible process), S = k lnw
H =
dQ
dt
= kA
TH − TC
L
, Hnet = Aeσ(T
4 − T 4s )
W = nCV (T1 − T2)
=
CV
R
(p1V1 − p2V2) (adiabatic process, ideal gas)
=
1
γ − 1(p1V1 − p2V2)
W = nRT ln
(
V2
V1
)
Reversible Processes for Ideal Gases:
Adiabatic (no heat transfer):
Q = 0, pV γ = constant, TV γ−1 = constant
Isochoric (constant volume): W = 0
Isobaric (constant pressure): W = p(V2 − V1)
Isothermal (constant temperature)
PHYS1001 Physics 1 (Regular)
Data and Formula Sheet
Data
Density of fresh water ρ = 1.00× 103 kg.m−3
Free fall acceleration at Earth’s surface g = 9.80 m.s−2
Gravitational constant G = 6.67× 10−11 N.m2.kg−2
Speed of light in a vacuum c = 3.00× 108 m.s−1
Speed of sound in air v = 344 m.s−1
Avogadro constant NA = 6.023× 1023 mol−1
Universal gas constant R = 8.314 J.mol−1.K−1
Boltzmann constant kB = 1.381× 10−23 J.K−1
Stefan-Boltzmann constant σ = 5.67× 10−8 W.m−2.K−4
Conversion of temperature scales 0◦C = 273.15 K
Oscillations
ω = 2pif =
2pi
T
, f =
ω
2pi
=
1
T
ω =
√
k
m
, ω =
√
κ
I
ω =
√
g
L
, ω =
√
mgd
I
Fx = −kx
x = A cos(ωt+ φ)
E =
1
2
mv2x +
1
2
kx2 =
1
2
kA2 = constant
x = Ae−(b/2m)t cosω′t, ω′ =
√
k
m
− b
2
4m2
bcritical = 2
√
km
A =
Fmax√(
k −mω2d
)2
+ b2ω2d
Longitudinal sound waves
v =
√
B
ρ
(fluid), v =
√
Y
ρ
(solid rod)
v =
√
γRT
M
(ideal gas)
fn =
nv
2L
(n = 1, 2, 3, . . .) (open pipe)
Mechanical waves
v = λf, k =
2pi
λ
ω = 2pif = vk, v =
√
F
µ
y(x, t) = A cos(kx± ωt)
y(x, t) = (ASW sin kx) sinωt (standing wave)
String fixed at both ends:
fn = n
v
2L
= nf1 (n = 1, 2, 3, . . .)
f1 =
1
2L
√
F
µ
β = (10 dB) log
I
I0
fn =
nv
4L
(n = 1, 3, 5, . . .) (stopped pipe)
fL =
v + vL
v + vS
fS (+ from L to S)
sinα =
v
vS
fbeat = |fa − fb|
PHYS1001 Semester 1, 2021 Page 2 of 2
Thermal physics
∆L = αL0∆T, ∆V = βV0∆T
Q = mc∆T, Q = nC∆T, Q = ±mL
pV = nRT = NkT N = nNA
CV =
3
2
R (ideal monatomic gas)
CV =
5
2
R (ideal diatomic gas)
CV = 3R (ideal monatomic solid)
CP = CV +R, γ =
CP
CV
vrms =
√
3RT
M
mtot = nM = nNAm
e =
W
QH
= 1 +
QC
QH
= 1−
∣∣∣∣QCQH
∣∣∣∣
eCarnot = 1− TC
TH
=
TH − TC
TH
KCarnot =
TC
TH − TC
eOtto = 1− 1
rγ−1
Ktr =
3
2
nRT,
1
2
m(v2)av =
3
2
kT
W =
∫ V2
V1
p dV, ∆U = Q−W
dU = dQ− dW (infinitesimal process)
K =
|QC |
|W | =
|QC |
|QH | − |QC |
∆S =
∫ 2
1
dQ
T
(reversible process), S = k lnw
H =
dQ
dt
= kA
TH − TC
L
, Hnet = Aeσ(T
4 − T 4s )
W = nCV (T1 − T2)
=
CV
R
(p1V1 − p2V2) (adiabatic process, ideal gas)
=
1
γ − 1(p1V1 − p2V2)
W = nRT ln
(
V2
V1
)
Reversible Processes for Ideal Gases:
Adiabatic (no heat transfer):
Q = 0, pV γ = constant, TV γ−1 = constant
Isochoric (constant volume): W = 0
Isobaric (constant pressure): W = p(V2 − V1)
Isothermal (constant temperature)
