Physics M20B
Exam 1
Fall 2022
Name:______________________________
General Math and Constants
sin Θ = (Opp/Hyp)
a2 + b2 = c2
A = 4πr2 (area of sphere)
cos Θ = (Adj/Hyp)
tan Θ = (Opp/Adj)
4
A = πr2 (area of circle)
Vol = πr3 (volume of sphere)
3
⃑⃑ • 𝑩
⃑⃑ = ABcosθ = AxBx + AyBy + AzBz
𝑨
R = 8.314 J/mol∙K = 0.08206 atm∙L
kB = 1.38 × 10-23 J/K
NA = 6.022 × 1023 particles/mole
1 atm = 101,300 Pa
1 m3 = 1000 L
Thermodynamics
∆L = αLi∆T
∆V = βVi∆T
β = 3α
pV = nRT = NkBT
Q = mc∆T
Q = Lf,v∆m
W = ∫ pdV
∆Eint = Q − W
𝑉2
W = p(V2 – V1) (isobaric process)
W = nRT ln(
1
1
̅̅̅2 ) = 3 NkBT = 3 nRT
Ktot trans = N( m0 𝑣
2
̅̅̅2 = 3 kBT
m0 𝑣
2
𝑉1
) (isothermal process)
2
Q = nCv∆T (isovolumetric process)
2
2
Q = nCp∆T (isobaric process)
∆Eint = nCv∆T (any process)
pVγ = constant (adiabatic process)
γ=
𝐶𝑃
CP = CV + R
𝐶𝑉
TVγ-1 = constant (adiabatic process)
𝑑
n = N/NA
CV = R
2
Heat Engines
e=
𝑊
𝑄ℎ
KR =
KR =
=1−
𝑄𝑐
𝑊
=
𝑄𝑐
𝑄ℎ
W = Qh − Qc
𝑄𝑐
𝑄ℎ − 𝑄𝑐
𝑇𝑐
𝑇ℎ − 𝑇𝑐
(Carnot refrigerator)
e=1−
KP =
KP =
𝑄ℎ
𝑊
𝑇𝑐
(Carnot efficiency)
𝑇ℎ
=
𝑄ℎ
𝑄ℎ − 𝑄𝑐
𝑇ℎ
𝑇ℎ − 𝑇𝑐
(Carnot heat pump)