Thermodynamics

{T_F=\frac{9}{5}T_C+32}

{T_K=T_C+273.15}

{\Delta L=\alpha L_0 \Delta T}                                        Linear Thermal Expansion

{\Delta V= \beta V_0 \Delta T}                                       Thermal Expansion of Volume

{PV=Nk_BT}                                 Ideal Gas Law

{P=P_{gauge} + 1 atm}

{PV=nRT}                                          Ideal Gas Law

{\frac{1}{2}mv_{rms}^2 = \frac{3}{2}k_B T}                    Average Kinetic Energy Per Molecule & Absolute Temperature

{\frac{Q}{t}=\frac{KA(T_2-T_1)}{d}}                          Rate of Heat Transfer Through Conduction

{\frac{Q}{t}=\sigma eAT^4}                          Rate of Heat Transfer Through Radiation

{\frac{Q}{t}=\sigma eA(T_2^4- T_1^4)}                          Net Rate of Heat Transfer Through Radiation

{Q=mc\Delta T}                     Heat Needed To Cause Change In Temperature

{Q=mL}                              Heat Needed To Cause Phase Change

{Q=\Delta U+W}               1st Law of Thermodynamics- Conservation of Energy

{U_{monatomic} = \frac{3}{2}Nk_B T= \frac{3}{2}nR T}           Internal Energy Of A Monatomic Gas

{U_{diatomic} = \frac{5}{2}Nk_B T=\frac{5}{2}nR T}           Internal Energy Of A Diatomic Gas

{work_{isobaric}=P\Delta V}                        Work Done In An Isobaric Process

{Work_{isothremal}=nRTln(\frac{V_2}{V_1})}                    Work In An Isothermal Process

{P_1V_1^\gamma = P_2V_2^\gamma}                        For An Adiabatic Process

\Delta S=\frac{Q}{T}               Change In Entropy At Constant Temperature

e=\frac{W}{Q_H}=1-\frac{|Q_C|}{Q_H}                               Efficiency Of A Heat Engine

e=1-\frac{T_C}{T_H}                            Efficiency Of An Ideal Carnot Engine

COP_{refrigerator}=\frac{|Q_C|}{|W|}

COP_{heat\ pump}=\frac{|Q_H|}{|W|}

COP_{ideal\ refrigerator}=\frac{T_C}{T_H - T_C}

COP_{ideal\ heat\ pump}=\frac{T_H}{T_H - T_C}

 

Electricity and Magnetism

|\vec F|=k\frac{|q_1| |q_2|}{r^2}                          Coulomb’s Law

\vec E=\frac{\vec F}{q}                                  Definition of Electric Field

|\vec E|=k\frac{|Q|}{r^2}                         Eelectric Field of A Point Charge

V=\frac{U_{electric}}{q}             Electric potential

V=k\frac{Q}{r}                                   Electric Potential Of A Point Charge

U_{electric}=k\frac{q_1 q_2}{r}          Potential Energy of Two Point Charges

|\Delta V|=|EdCos\theta|                                        In A Constant Electric Field

|\Delta V|=EL\ ,\ E=\frac{\Delta V}{L}                            In A Constant Electric Field

Q=C\Delta V                   Charge On A Capacitor

C=\epsilon_0 \frac{A}{d}                       Capacitance Of Air-Filled Parallel Plate Capacitor

U=\frac{1}{2}Q\Delta V = \frac{1}{2}\frac{Q^2}{C}=\frac{1}{2}C(\Delta V)^2                           Energy Stored In A Charged Capacitor

\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+.....                                 Capacitors In Series

C_{eq}=C_1+C_2+C_3+...                            Capacitors In Parallel

I=\frac{\Delta q}{\Delta t}                                 Electric Current

I=nqAv_d                                Current In Terms Of Drift Speed

I=\frac{\Delta V}{R}                                  Ohm’s Law

R=\rho \frac{L}{A}                                 Resistance Of A Conductor

P=I \Delta V                            Electric Power

R_{eq}=R_1 + R_2 + R_3+.....                                 Resistors In Series

\frac{1}{R_{eq}}=\frac{1}{R_1} + \frac{1}{R_2} +\frac{1}{R_3}+...                              Resistors In Parallel

\Delta V=emf- Ir                                           Terminal Voltage Of A Battery

{|\vec F|=|q||\vec v||\vec B|sin\theta}                   Magnetic Force On A Moving Charge

{F=IlBsin\theta}                               Force On A Current Carrying Wire

{B=\frac{\mu_0 I}{2\pi r}}                      Magnetic Filed Of A Long Straight Current

{B=\frac{\mu_0 I}{2R}}            Magnetic Filed At The Center Of A Current Loop

{B=\mu_0 nI}            Magnetic Filed Inside Of A Solenoid

\mu_0=4\pi \times 10^{-7}Tm/A

Light and Optics

c=\lambda f                                  Speed Of Electromagnetic Waves In Vacuum

n=\frac{c}{v}              Index Of Refraction

n_1sin\theta_1=n_2sin\theta_2                         The Law Of Refraction

f=\frac{R}{2}                   Focal Length Of Spherical Mirrors

\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}                     Mirror Equation and Thin Lens Equation

M=\frac{h_i}{h_o}=-\frac{d_i}{d_o}          Lateral Magnification

\frac{1}{f}=(n-1)(\frac{1}{R_1}-\frac{1}{R_2})       Lens Makers Equation

P=\frac{1}{f}               Optical Power

 

 

 

 

 

 

 

 

 

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