web viewwork done by universe: w= t c ∆ s universe electric force, field, flux. electric force:...
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Heat Engines, Entropy
Work done by heat engine: W=Qh−|Q c|
Efficiency of heat engine: e=WQh
=1−|Qc|Qh
Energy: ∆U=Q−W=T ∆S−P∆V
Carnot engine (max) efficiency: emax=1−T c∆ Sc
Th∆ Sh=1−
T c
T h
Carnot engine (max) work: W=emaxQh
Coefficient of performance: COP fridge , AC=Qc
W
COPheat pump=Qh
W
Entropy: ∆ S=QT
Entropy of heat engine: ∆ S=∆ Sh−∆Sc=Qh
Th−Q c
T c
Work done by universe: W=Tc∆ Suniverse
Electric Force, Field, Flux
Electric force: F⃑=k|q1||q2|
r 2
o Force points away from positive charges!
o Vector sum: Find magnitude of each force
Find components of each force: F x=Fcosθ and F y=Fsinθ
Add all x components and all y components
Find magnitude of net force: F=√F x2+F y
2
Find direction of net force θ by SOHCAHTOA
o Electric force of a sphere: F⃑=k|q||Q|
r2 =k|q|σA
r2
Electric field: E⃑= F⃑q0
o Field points away from positive charges!
o Vector sum: Find magnitude of each field
Find components of each field: E x=Ecosθ and E y=Esinθ
Add all x components and all y components
Find magnitude of net field: E=√E x2+Ey
2
Find direction of net field θ by SOHCAHTOA
Dipole: p=qd
Electric flux (through an area A tilted at angle θ): Ф=EAcosθ
o Flux is positive as it leaves the enclosed volume of the surface!
o Electric flux through a spherical surface: φ=EA=4 πkq=qenclosed
ε0
o Electric flux of a point charge inside a sphere: φ=4 π r2 E=qenclosed
ε0
o Gaussian wire of charge λ C/m: φ=2πrLE= λLε 0
o Gaussian cylinder through a plate of charge σ C/m2: φ=2 EA= σAε 0
Electric field of a Gaussian surface:
o Inside a sphere: E= kQr1
2
o Within a sphere: E=0
o Surrounding a sphere: E= kQr3
2
o Infinite plate/sheet: E= σ2ε 0
o Parallel plate: E= Qε0 A
o Plates of opposite charges: Figure
Work done by electric force: W=−q0Ed
Electric Potential, Potential Energy, Capacitance
Electric potential energy: ∆U=−W=q0Ed
U=k q0qr
o Net potential energy is the algebraic sum (NOT vector!)
Electric potential: ∆V=∆Uq0
o For a point charge: ∆V= kqr
o For a sphere: ∆V=4 πkσR= kQR
o For multiple charges: V=kΣqi
|r−ri|
Electric field: E=−∆V∆ s
Conservation of energy: K A+U A =K B+UB
o Kinetic energy: K=12mv2
o Potential energy: U=qV
Capacitance: C=QV
o Parallel plate: C=ε0 Ad
o Parallel plate + dielectric (insulator in between): C=κ ε 0 Ad
o Capacitors in series: 1Ceq
=∑ 1C i
o Capacitors in parallel: C eq=∑ Ci
Energy stored in a capacitor: U=12QV=1
2CV 2=Q 2
2C
o Parallel plate: U=12ε0 E
2 Ad=uE Ad where uE=12ε0E
2 or uE=
UΩ
=12κ ε0 E
2 for a dielectric