Physics 1710 Section 004 Mechanics and Thermodynamics Final Review.

Physics 1710Physics 1710Section 004Section 004

Mechanics and Mechanics and ThermodynamicsThermodynamics

Final ReviewFinal Review

Physics 1710Physics 1710Section 004Section 004

Mechanics and Mechanics and ThermodynamicsThermodynamics

Final ReviewFinal Review

Physics 1710Physics 1710MWF Session 1 IntroductionMWF Session 1 Introduction

The “Structure” of this course:The “Structure” of this course:

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ics

Dyn

am

ics

KinematicsKinematics

ApplicationsApplicationsStaticsStaticsElasticitElasticit

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GravitatioGravitationn

Fluid Fluid MechanicsMechanics

OscillationsOscillationsWavesWaves

ThermodynamThermodynamicsics

SummarySummary•Fundamental Fundamental DimensionsDimensions and and UnitsUnits

TimeTime, measured in , measured in secondsseconds;;

LengthLength, measured in, measured in metersmeters;;

MassMass, measured in , measured in kilogramskilograms..

• PrefixesPrefixes scale units to convenient size. scale units to convenient size.k =1000, M = 1 000 000k =1000, M = 1 000 000c = 1/100, m = 1/1000, c = 1/100, m = 1/1000, μ =1/1 000 000μ =1/1 000 000

• DensityDensity is mass per unit volume. is mass per unit volume.ρ = m/V ρ = m/V [[kg/mkg/m3 3 ]]

• Avogadro’s numberAvogadro’s number is the number of atoms is the number of atoms in a mole of an element. in a mole of an element. 6.022 x106.022 x102323 atom/mole atom/mole

Physics 1710Physics 1710—C—Chapter 1 Measurementhapter 1 Measurement

• The change in the instantaneous velocity is equal to The change in the instantaneous velocity is equal to the (constant) acceleration multiplied by its duration. the (constant) acceleration multiplied by its duration. ∆v = at∆v = at

•The displacement is equal to the displacement at The displacement is equal to the displacement at constant velocity plus one half of the product of the constant velocity plus one half of the product of the acceleration and the square of its duration. acceleration and the square of its duration. ∆x = ∆x = vvinitialinitial t + ½ at t + ½ at 22

•The change in the square of the velocity is equal to The change in the square of the velocity is equal to two times the acceleration multiplied by the distance two times the acceleration multiplied by the distance traveled during acceleration. traveled during acceleration. ∆v ∆v 22 = 2a ∆x = 2a ∆x

•The acceleration of falling bodies is 9.8 m/s/s The acceleration of falling bodies is 9.8 m/s/s downward.downward.

a = - g = - 9.8 m/s/sa = - g = - 9.8 m/s/s

Summary:Summary:

Physics 1710Physics 1710Chapter 2 Motion in One Dimension—II Chapter 2 Motion in One Dimension—II

Summary:Summary:

•To add vectors, simply add the components To add vectors, simply add the components separately.separately.

•Use the Pythagorean theorem for the magnitude.Use the Pythagorean theorem for the magnitude.

•Use trigonometry to get the angle.Use trigonometry to get the angle.

•The vector sum will always be equal or less than The vector sum will always be equal or less than the arithmetic sum of the magnitudes of the the arithmetic sum of the magnitudes of the vectors.vectors.

Physics 1710Physics 1710 Chapter 3 Vectors Chapter 3 Vectors

Summary:Summary:• Kinematics in two (or more) dimensions obeys Kinematics in two (or more) dimensions obeys the same 1- D equations in each component the same 1- D equations in each component independently. independently.

– rrfinalfinal = = rrinitialinitial + v + vinitialinitial tt + + ½ ½ a a t t 22

– vvfinalfinal == vvinitialinitial + a + a t t – vvx,finalx,final

22 = v = vx,initialx,initial 22+ 2 a+ 2 axx / /∆x∆x– vvy,finaly,final

22 = v = vy,initialy,initial 22+ 2 a+ 2 ayy / /∆y∆y

• Projectiles follow a parabola [y(x) = A + Bx Projectiles follow a parabola [y(x) = A + Bx +Cx+Cx22]]

Physics 1710Physics 1710 Chapter 4: 2-D Chapter 4: 2-D Motion—II Motion—II

Summary:Summary:

• In a moving or accelerating Frame of In a moving or accelerating Frame of ReferenceReference

• v v ′ ′ = = v – v v – vframe of referenceframe of reference

• a a ′ ′ = = a – a a – aframe of referenceframe of reference

• The The CentripetalCentripetal acceleration is acceleration is

• a = - a = - ω2 rr

or or ||aa| | = v = v 22/ / |r|,|r|, toward the center. toward the center.

Physics 1710Physics 1710 Chapter 4: 2-D Chapter 4: 2-D Motion—II Motion—II

Summary:Summary:• Newton’s Laws of Motion are:Newton’s Laws of Motion are:

(1) Acceleration (or deceleration) occurs if (1) Acceleration (or deceleration) occurs if and only if there is a net external and only if there is a net external forceforce..

(2)(2) a a = = FF//m m [Note this is a vector eqn.][Note this is a vector eqn.]

(3) The force exerted by a first object on a (3) The force exerted by a first object on a second is second is always always equal and opposite the the equal and opposite the the force exerted by the second on the first. force exerted by the second on the first. FF1212 = = - F- F2121

Physics 1710Physics 1710 Chapter 5: Laws of Chapter 5: Laws of Motion—II Motion—II

Summary (cont’d.) :Summary (cont’d.) :

• Weight is the force of gravity equal to Weight is the force of gravity equal to gg times times the mass of the object.the mass of the object.

• gg =9.80 =9.80 N/kgN/kg

• The force of friction is opposed to the motion The force of friction is opposed to the motion of a body and proportional to the of a body and proportional to the normal normal forceforce..

• Free body diagrams are sketches of all the Free body diagrams are sketches of all the forces acting on a bodyforces acting on a body..

Physics 1710Physics 1710 Chapter 5: Laws of Chapter 5: Laws of Motion—II Motion—II

Summary Summary • The net force on a body executing circular The net force on a body executing circular motion is equal to the mass times the centripetal motion is equal to the mass times the centripetal acceleration of the body.acceleration of the body.

•aacentripedalcentripedal = = v v 22/ R/ R [toward the center] [toward the center]

• The “centrifugal” force is a fictitious force due to The “centrifugal” force is a fictitious force due to a non-inertial frame of reference.a non-inertial frame of reference.

Physics 1710Physics 1710 Chapter 6—Circular Chapter 6—Circular Motion Motion

Summary Summary • Work is defined to be the distance Work is defined to be the distance traveled multiplied by the distance over traveled multiplied by the distance over which the force acts.which the force acts.

• W = W = ∫ ∫ F•F•d d rr

•[Joules] = [N ][m][Joules] = [N ][m]

Physics 1710Physics 1710 Chapter 7—Work Chapter 7—Work

Summary:Summary:

•The Potential Energy is equal to the The Potential Energy is equal to the negative of the work done on the system to negative of the work done on the system to put it in its present state.put it in its present state.

U = -U = -∫ F•d r∫ F•d r• The sum of all energy, potential and The sum of all energy, potential and kinetic, of a system is conserved, in the kinetic, of a system is conserved, in the absence of dissipation.absence of dissipation.

E = U + K – WE = U + K – W• F = - F = - ∇U∇U

•P P = = dE/dtdE/dt

Physics 1710Physics 1710 Chapter 7&8—Power & Chapter 7&8—Power & EnergyEnergy

SummarySummary

• F = - F = - ∇∇U = negative gradient of U.U = negative gradient of U.

• The Potential Energy graph is a The Potential Energy graph is a complete description of the dynamics complete description of the dynamics of a system.of a system.

Physics 1710Physics 1710—C—Chapter 1 Measurementhapter 1 Measurement

Summary:Summary:•Angular displacement is the angle Angular displacement is the angle through which a body has rotated.through which a body has rotated.

•Instantaneous angular speed is the time Instantaneous angular speed is the time rate of angular displacement.rate of angular displacement.

•Instantaneous angular acceleration is Instantaneous angular acceleration is the time rate of change in angular speed.the time rate of change in angular speed.

Physics 1710Physics 1710—C—Chapter 10 Rotating hapter 10 Rotating BodiesBodies

SummarySummary (cont’d): (cont’d):•The moment of inertia is the measure of The moment of inertia is the measure of the (inertial) resistance to angular the (inertial) resistance to angular acceleration and equal to the second acceleration and equal to the second moment of the mass distribution.moment of the mass distribution.

•Torque (“twist”) is the vector product of Torque (“twist”) is the vector product of a force and the “moment” arm.a force and the “moment” arm.


Summary:Summary:

•The moment of inertia I is the measure of The moment of inertia I is the measure of the (inertial) resistance to angular the (inertial) resistance to angular acceleration and equal to the second acceleration and equal to the second moment of the mass distribution about an moment of the mass distribution about an axis.axis.


Summary:Summary:

•The total Kinetic energy of a rotating system is The total Kinetic energy of a rotating system is the sum of the rotational energy about the Center the sum of the rotational energy about the Center of Mass and the translational KE of the CM. of Mass and the translational KE of the CM.

K = ½ IK = ½ ICMCM ⍵ ⍵ 22 + + ½ MR½ MR 2 2 ⍵ ⍵ 22

ττ = r x F = r x F


Summary:Summary:


•Angular momentum Angular momentum LL is the vector product of is the vector product of the moment arm and the linear momentum.the moment arm and the linear momentum.

L = r L = r x x pp

• The net externally applied torque is equal to The net externally applied torque is equal to the time rate of change in the angular the time rate of change in the angular

momentum.momentum.

∑ ∑ ττzz = d L = d Lzz /dt = I /dt = Izz ⍺ ⍺

SummarySummary• Rotary (circular) motion obeys laws that are Rotary (circular) motion obeys laws that are analogous to those of translational motion.analogous to those of translational motion.

• Linear Momentum is conserved in absence of Linear Momentum is conserved in absence of external forces.external forces.

• F = F = d d pp/dt/dt

• Energy is related to the work done or storedEnergy is related to the work done or stored• Work is the cumulative force times distance Work is the cumulative force times distance moved.moved.• Power is the rate of expenditure of work or Power is the rate of expenditure of work or energy.energy.• Force is the negative of the gradient of the Force is the negative of the gradient of the potential.potential.

Physics 1710Physics 1710—C—Chapters 6-10hapters 6-10

SummarySummary::• Angular momentum about an axis z is equal to Angular momentum about an axis z is equal to the product of the moment of inertia of the body the product of the moment of inertia of the body about that axis and the angular velocity about z.about that axis and the angular velocity about z.

L =L = I I ⍵⍵

LLzz = I = Izz ⍵⍵

• In the absence of torques, the angular In the absence of torques, the angular momentum is conserved.momentum is conserved.

• In the presence of torques the angular moment In the presence of torques the angular moment will change with time.will change with time.


SummarySummary

• Static equilibrium implies that all forces Static equilibrium implies that all forces and torques balance.and torques balance.

• The center of mass is often the center of The center of mass is often the center of gravity.gravity.

• The moduli of elasticity characterizes the The moduli of elasticity characterizes the stress-strain relation:stress-strain relation:

• stress= modulus x strainstress= modulus x strainStress = modulus x strainStress = modulus x strain

σ = σ = F/A = Y F/A = Y εε

Physics 1710Physics 1710—C—Chapter 11 App: E & Ehapter 11 App: E & E

SummarySummary::

• The force of attraction between two bodies The force of attraction between two bodies with mass M and m respectively is proportional with mass M and m respectively is proportional to the product of their masses and inversely to the product of their masses and inversely proportional to the distance between their proportional to the distance between their centers squared.centers squared.

F = - G M m/ r F = - G M m/ r 22

• The proportionality constant in the Universal The proportionality constant in the Universal Law of Gravitation G is equal to 6.673 x 10 Law of Gravitation G is equal to 6.673 x 10 –11–11 N N mm22 /kg /kg22 . .

Physics 1710Physics 1710—C—Chapter 13 Apps: Gravityhapter 13 Apps: Gravity

Summary:Summary:•The gravitational force constant g is equal to The gravitational force constant g is equal to G M/(R+h) G M/(R+h) 22, R is the radius of the planet., R is the radius of the planet.

• Kepler’s LawsKepler’s Laws–The orbits of the planets are ellipses.The orbits of the planets are ellipses.–The areal velocity of a planet is constant.The areal velocity of a planet is constant.–The cube of the radius of a planet’s orbit The cube of the radius of a planet’s orbit is proportional to the square of the period.is proportional to the square of the period.

• The gravitation field is the force divided by the The gravitation field is the force divided by the mass.mass.

g g = = FFgg / m / m


SummarySummary::

• The force of attraction between two bodies The force of attraction between two bodies with mass M and m respectively is proportional with mass M and m respectively is proportional to the product of their masses and inversely to the product of their masses and inversely proportional to the distance between their proportional to the distance between their centers squared.centers squared.

F = - G M m/ r F = - G M m/ r 22

• The proportionality constant in the Universal The proportionality constant in the Universal Law of Gravitation G is equal to 6.673 x 10 Law of Gravitation G is equal to 6.673 x 10 –11–11 N N mm22 /kg /kg22 . .


Summary:Summary:

• The gravitation potential energy for a point mass is The gravitation potential energy for a point mass is proportional to the product of the masses and proportional to the product of the masses and inversely proportional to the distance between their inversely proportional to the distance between their centers:centers:

U = GMm / rU = GMm / r

• The escape velocity is the minimum speed a The escape velocity is the minimum speed a projectile must have at the surface of a planet to projectile must have at the surface of a planet to escape the gravitational field.escape the gravitational field.

vvescape escape = = √[ 2GM/R]√[ 2GM/R]

• Total Energy E is conserved for two body Total Energy E is conserved for two body geavitational problem; bodies are bound for E ≤ 0geavitational problem; bodies are bound for E ≤ 0

E = LE = L22/2mr/2mr 2 2 – GMm/r – GMm/r


Summary: Summary: •Pressure Pressure is the force per unit area. P =F/A is the force per unit area. P =F/A

• Unit of pressure [Pacal] = [N]/[mUnit of pressure [Pacal] = [N]/[m22]]

•The The hydrostatic pressurehydrostatic pressure is P = P is P = Poo + + ρρghgh

• Archimedes’ PrincipleArchimedes’ Principle: F: Fbouyant bouyant = = ρρfluid fluid g Vg V

• Equation of ContinuityEquation of Continuity: A: A11vv11 = A = A22vv22

• Bernoulli’s Equation:Bernoulli’s Equation: P + ½ ρvP + ½ ρv22 + ρgy = + ρgy = constant.constant.

Physics 1710Physics 1710—C—Chapter 14 Fluid hapter 14 Fluid DynamicsDynamics

Summary : Summary :

• Simple Harmonic Motion is sinusoidal. Simple Harmonic Motion is sinusoidal. x = Xx = Xoo cos(cos(ωt +φ)ωt +φ)

• The period is the reciprocal of the frequency.The period is the reciprocal of the frequency. T = 1/ T = 1/

ff• For a mass m on a spring of spring constant k, For a mass m on a spring of spring constant k,

the period the period T = T = 22ππ√(m/k)√(m/k)

• For Damped SHO, the frequency is decreased For Damped SHO, the frequency is decreased and the amplitude decays exponentially.and the amplitude decays exponentially.

x = x = XXoo e e – ½ (b/m)t– ½ (b/m)t cos( cos(ωt +φ)ωt +φ)with with ω = ω = √[√[k/m – ½ b/m]k/m – ½ b/m]

Physics 1710Physics 1710—C—Chapter 15 SHOhapter 15 SHO

Summary : Summary :

• For a driven SHO the amplitude is a maximum For a driven SHO the amplitude is a maximum when the drive frequency is equal to the natural when the drive frequency is equal to the natural frequency; a condition known as “resonance.”frequency; a condition known as “resonance.”

• A simple pendulum oscillates at a frequency of A simple pendulum oscillates at a frequency of

ff = (1/2 = (1/2π) π) √(g/L)√(g/L)

•A physical pendulum oscillates at a frequency of A physical pendulum oscillates at a frequency of

ff = (1/2 = (1/2π) π) √(mgL/I)√(mgL/I)

Physics 1710Physics 1710—C—Chapter 15 SHOhapter 15 SHO

Summary : Summary : • A traveling wave has the formA traveling wave has the form

y(x,t) = Y sin(kx y(x,t) = Y sin(kx –– ωt),ωt), with with k = 2π/λk = 2π/λ, , k k : wave number, : wave number, λλ : :

wavelengthwavelength& & ω= 2π ω= 2π f f = 2π/ = 2π/ TT as previously definedas previously defined

• d d 22y/dx y/dx 22 = (1/v = (1/v 22) d ) d 22y/dt y/dt 22 is the is the linear wave linear wave equation.equation.

• λ λ ff = v = v, the phase velocity., the phase velocity.

• For a longitudinal wave on a string For a longitudinal wave on a string v = v = √(√(TT//μ).μ). TT = tension, = tension, μμ = dm/dx = linear mass density = dm/dx = linear mass density

• The time averaged The time averaged power power transmitted on a string transmitted on a string is is

₧ = ½ ₧ = ½ μ ωμ ω22AA22vv

Physics 1710Physics 1710—C—Chapter 16 Waveshapter 16 Waves

Summary : Summary :

• Sound is a longitudinal pressure/displacementSound is a longitudinal pressure/displacement

•V = V = √B/√B/ρρ, the phase velocity is equal to the square , the phase velocity is equal to the square root of the ratio of the bulk modulus to the density.root of the ratio of the bulk modulus to the density.

• The Doppler effect is a shift in frequency due to the The Doppler effect is a shift in frequency due to the relative motion of the source and observer of a relative motion of the source and observer of a sound.sound.

Physics 1710Physics 1710—C—Chapter 17 Soundhapter 17 Sound

Summary : Summary : • A traveling wave has the formA traveling wave has the form

y(x,t) = Y sin(kx y(x,t) = Y sin(kx –– ωt),ωt), with with k = 2π/λk = 2π/λ, , k k : wave number, : wave number, λλ : :

wavelengthwavelength& & ω= 2π ω= 2π f f = 2π/ = 2π/ TT as previously definedas previously defined

• d d 22y/dx y/dx 22 = (1/v = (1/v 22) d ) d 22y/dt y/dt 22 is the is the linear wave linear wave equation.equation.

• λ λ ff = v = v, the phase velocity., the phase velocity.

• For a longitudinal wave on a string For a longitudinal wave on a string v = v = √(√(TT//μ).μ). TT = tension, = tension, μμ = dm/dx = linear mass density = dm/dx = linear mass density

• The time averaged The time averaged power power transmitted on a string transmitted on a string is is

₧ = ½ ₧ = ½ μ ωμ ω22AA22vv

Physics 1710Physics 1710—C—Chapter 16 Waveshapter 16 Waves

Summary:Summary:The propagation of waves is characterized by The propagation of waves is characterized by

ReflectionReflection — the rebound of the wave. — the rebound of the wave.

Refraction Refraction — the bending of a wave’s — the bending of a wave’s direction due to a velocity direction due to a velocity

gradientgradient

Diffraction Diffraction — the bending of a wave — the bending of a wave around obstacles.around obstacles.

InterferenceInterference — the combination of two — the combination of two or more waves in space.or more waves in space.

BeatsBeats — the combination of two waves — the combination of two waves in time.in time.

Physics 1710Physics 1710—C—Chapter 18 hapter 18 Chapter 18 Chapter 18 Superposition and Standing WavesSuperposition and Standing Waves

Summary:Summary:

• Angle of incidence = angle of reflection; Angle of incidence = angle of reflection;

θθ ii = = θθ rr

• sin sin θθ 11 /v /v11 = sin = sin θθ 22 / v / v22

• ffaveave = (= ( f f11 + f + f22 )/2; )/2; ffbeatbeat = (= ( f f11 - f - f22 ))

• ffnn = = n /(2L) n /(2L) √(T/√(T/μμ))• A = (A = (FFextext /m)/ [ω/m)/ [ω00 22 - ω - ω22] ]

Physics 1710Physics 1710—C—Chapter 18 hapter 18 Chapter 18 Chapter 18 Superposition and Standing WavesSuperposition and Standing Waves

Physics 1710Physics 1710Chapter 19 TemperatureChapter 19 Temperature

Summary:Summary:•Temperature is a measure of the average Temperature is a measure of the average kinetic energy of a system of particles.kinetic energy of a system of particles.

• Thermal Equilibrium means that two bodies Thermal Equilibrium means that two bodies are at the same temperature.are at the same temperature.

• The “Zeroth Law of Thermodynamics” states The “Zeroth Law of Thermodynamics” states that if system A and B are n thermal equilibrium that if system A and B are n thermal equilibrium with system C, then A and B are in thermal with system C, then A and B are in thermal Equilibrium with each other.Equilibrium with each other.

Physics 1710Physics 1710Chapter 19 TemperatureChapter 19 Temperature

•Kelvin is a unit of temperature where Kelvin is a unit of temperature where one degree K is 1/279.16 of the one degree K is 1/279.16 of the temperature of the triple point of water temperature of the triple point of water (near freezing).(near freezing).

TTC C = (100/180) (T= (100/180) (TFF – 32 – 32 ⁰F⁰F))

TTF F = (180/100) T= (180/100) TC C + 32 + 32 ⁰F⁰F• ∆∆L/L = L/L = αα∆T∆T• PV = n R T = N kTPV = n R T = N kT

SummarySummary•The internal energy is the total average The internal energy is the total average energy of the atoms of an object.energy of the atoms of an object.

• Heat is the change in internal energy.Heat is the change in internal energy.

• The change in temperature is proportional to The change in temperature is proportional to the change in internal energy (heat flow) when the change in internal energy (heat flow) when there is no change of phase and the system there is no change of phase and the system does no work.does no work.

• The first law of thermodynamics states The first law of thermodynamics states

∆∆E = ∆Q - WE = ∆Q - W

Physics 1710Physics 1710 C Chapter 20 Heat & 1hapter 20 Heat & 1stst Law of Law of ThermoThermo

SummarySummary::

• The Ideal Gas Law results from the cumulative The Ideal Gas Law results from the cumulative action of atoms or molecules.action of atoms or molecules.

• The average kinetic energy of the atoms or The average kinetic energy of the atoms or molecules of an ideal gas is equal to 3/2 kT.molecules of an ideal gas is equal to 3/2 kT.

½ m<v½ m<v22> = 3/2 kT> = 3/2 kT

• Energy average distributes equally (is Energy average distributes equally (is equipartitioned) into all available states. equipartitioned) into all available states.

•Each degree of freedom contributes 1/2 kT to the Each degree of freedom contributes 1/2 kT to the energy of a system.energy of a system.

Physics 1710Physics 1710 Chapter 21 Kinetic theory of Chapter 21 Kinetic theory of GasesGases

Summary (cont’d.)Summary (cont’d.)

γγ = C = CP P / C/ CVV

PV PV γγ = constant= constantB = B = γγ P P

• The distribution of particles among available The distribution of particles among available energy states obeys the Boltzmann distribution energy states obeys the Boltzmann distribution law.law.

nnVV = n = noo e e –E/kT–E/kT

Physics 1710Physics 1710 Chapter 21 Kinetic theory of Chapter 21 Kinetic theory of GasesGases

Physics 1710Physics 1710Chapter 22 Heat Engines etcChapter 22 Heat Engines etc

Summary:Summary:•The work done by a heat engine is The work done by a heat engine is equal to the difference in the heat equal to the difference in the heat absorbed at the high temperature and absorbed at the high temperature and expelled at the low.expelled at the low.

∆∆W = ∆QW = ∆Qhh – ∆Q – ∆Qcc

• The thermal efficiency is the work done The thermal efficiency is the work done divided by the heat absorbed.divided by the heat absorbed.

e = 1 - ∆Qe = 1 - ∆Qc c / ∆Q/ ∆Qh h


Summary:Summary:• Kelvin-Planck form of 2 Kelvin-Planck form of 2 nd nd Law of Law of Thermo: It is impossible to construct a Thermo: It is impossible to construct a heat engine that, operating in a cycle, heat engine that, operating in a cycle, produces no effect other than the produces no effect other than the absorption of energy from a reservoir and absorption of energy from a reservoir and the performance of an equal amount of the performance of an equal amount of work. work. •Clausius Form of 2 Clausius Form of 2 nd nd Law of Thermo: It Law of Thermo: It is impossible to construct a cyclical is impossible to construct a cyclical machine whose sole effect is the machine whose sole effect is the continuous transfer of energy from one continuous transfer of energy from one object to another at a higher object to another at a higher temperature without the input of work.temperature without the input of work.


Summary:Summary:•The maximum efficiency is obtained via The maximum efficiency is obtained via a Carnot cycle and is equal to the a Carnot cycle and is equal to the temperature difference divided by the temperature difference divided by the high temperature.high temperature.

eeCarnot Carnot = 1 - T= 1 - Tc c / T/ Thh

• Entropy S is a measure of the disorder Entropy S is a measure of the disorder of a system.of a system.• ∆ ∆S = ∫dQ/TS = ∫dQ/T• S≡ k ln NS≡ k ln N

Physics 1710 Section 004 Mechanics and Thermodynamics Final Review.

Documents

force of gravity equal

net force

fictitious force

centrifugal force

normal force

force of friction

force acts

constant acceleration