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PHYS 2310 Engineering Physics I Formula Sheets Chapters 1-18
Chapter 1/Important Numbers
Chapter 2
Units for SI Base Quantities
Quantity Unit Name Unit Symbol
Length Meter M
Time Second s
Mass (not weight) Kilogram kg
Common Conversions
1 kg or 1 m 1000 g or m 1 m 1 Γ 106 ππ 1 m 100 cm 1 inch 2.54 cm
1 m 1000 mm 1 day 86400 seconds
1 second 1000 milliseconds 1 hour 3600 seconds
1 m 3.281 ft 360Β° 2π rad
Important Constants/Measurements
Mass of Earth 5.98 Γ 1024 kg
Radius of Earth 6.38 Γ 106 m
1 u (Atomic Mass Unit) 1.661 Γ 10β27 kg
Density of water 1 π/ππ3 or 1000 ππ/π3
g (on earth) 9.8 m/s2
Density
Common geometric Formulas
Circumference πΆ = 2ππ Area circle π΄ = ππ2
Surface area (sphere)
ππ΄ = 4ππ2 Volume (sphere) π =4
3ππ3
Volume (rectangular solid) π = π β π€ β β
π = ππππ β π‘βππππππ π
Velocity
Average Velocity πππ£π =πππ πππππππππ‘
π‘πππ=
βπ₯
βπ‘ 2.2
Average Speed π ππ£π =π‘ππ‘ππ πππ π‘ππππ
π‘πππ 2.3
Instantaneous Velocity π£ = limβπ‘β0
βοΏ½Μ οΏ½
βπ‘=
ππ₯
ππ‘ 2.4
Acceleration
Average Acceleration πππ£π =βπ£
βπ‘ 2.7
Instantaneous Acceleration
π =ππ£
ππ‘=
π2π₯
ππ‘2
2.8 2.9
Motion of a particle with constant acceleration
π£ = π£0 + ππ‘ 2.11
βπ₯ =1
2(π£0 + π£)π‘ 2.17
βπ₯ = π£0π‘ +1
2ππ‘2 2.15
π£2 = π£02 + 2πβπ₯ 2.16
Chapter 3
Chapter 4
Adding Vectors Geometrically οΏ½βοΏ½ + οΏ½ββοΏ½ = οΏ½ββοΏ½ + οΏ½βοΏ½ 3.2
Adding Vectors Geometrically (Associative Law)
(οΏ½βοΏ½ + οΏ½ββοΏ½) + π = οΏ½βοΏ½ + (οΏ½ββοΏ½ + π) 3.3
Components of Vectors ππ₯ = ππππ π ππ¦ = ππ πππ
3.5
Magnitude of vector |π| = π = βππ₯2 + ππ¦
2 3.6
Angle between x axis and vector
π‘πππ =ππ¦
ππ₯ 3.6
Unit vector notation οΏ½βοΏ½ = ππ₯πΜ + ππ¦πΜ + ππ§οΏ½ΜοΏ½ 3.7
Adding vectors in Component Form
ππ₯ = ππ₯ + ππ₯ ππ¦ = ππ¦ + ππ¦
ππ§ = ππ§ + ππ§
3.10 3.11 3.12
Scalar (dot product) οΏ½βοΏ½ β οΏ½ββοΏ½ = πππππ π 3.20
Scalar (dot product) οΏ½βοΏ½ β οΏ½ββοΏ½ = (ππ₯πΜ + ππ¦πΜ + ππ§οΏ½ΜοΏ½) β (ππ₯πΜ + ππ¦πΜ + ππ§οΏ½ΜοΏ½)
οΏ½βοΏ½ β οΏ½ββοΏ½ = ππ₯ππ₯ + ππ¦ππ¦ + ππ§ππ§ 3.22
Projection of οΏ½βοΏ½ ππ οΏ½ββοΏ½ or
component of οΏ½βοΏ½ ππ οΏ½ββοΏ½
οΏ½βοΏ½ β οΏ½ββοΏ½
|π|
Vector (cross) product magnitude
π = πππ πππ 3.24
Vector (cross product)
οΏ½βοΏ½π₯οΏ½ββοΏ½ = (ππ₯πΜ + ππ¦πΜ + ππ§οΏ½ΜοΏ½)π₯(ππ₯πΜ + ππ¦πΜ + ππ§οΏ½ΜοΏ½)
= (ππ¦ππ§ β ππ¦ππ§)πΜ + (ππ§ππ₯ β ππ§ππ₯)πΜ
+ (ππ₯ππ¦ β ππ₯ππ¦)οΏ½ΜοΏ½
or
οΏ½βοΏ½π₯οΏ½ββοΏ½ = πππ‘ |
πΜ π οΏ½ΜοΏ½ππ₯ ππ¦ ππ§
ππ₯ ππ¦ ππ§
|
3.26
Position vector π = π₯πΜ + π¦πΜ + π§οΏ½ΜοΏ½ 4.4
displacement βπ = βπ₯πΜ + βπ¦πΜ + βπ§οΏ½ΜοΏ½ 4.4
Average Velocity οΏ½ββοΏ½ππ£π =βπ₯
βπ‘ 4.8
Instantaneous Velocity οΏ½βοΏ½ =ππ
ππ‘= π£π₯ οΏ½ΜοΏ½ + π£π¦πΜ + π£π§οΏ½ΜοΏ½
4.10 4.11
Average Acceleration οΏ½βοΏ½ππ£π =βοΏ½βοΏ½
βπ‘ 4.15
Instantaneous Acceleration
οΏ½βοΏ½ =ποΏ½βοΏ½
ππ‘
οΏ½βοΏ½ = ππ₯πΜ + ππ¦πΜ + ππ§οΏ½ΜοΏ½
4.16 4.17
Projectile Motion
π£π¦ = π£0π πππ0 β ππ‘ 4.23
βπ₯ = π£0πππ ππ‘ +1
2ππ₯π‘2
or βπ₯ = π£0πππ ππ‘ if ππ₯=0
4.21
βπ¦ = π£0π ππππ‘ β1
2ππ‘2 4.22
π£π¦2 = (π£0π πππ0)2 β 2πβy 4.24
π£π¦ = π£0π πππ0 β ππ‘ 4.23
Trajectory π¦ = (π‘πππ0)π₯ βππ₯2
2(π£0πππ π0)2 4.25
Range π =π£0
2
πsin(2π0) 4.26
Relative Motion
π£π΄πΆββ ββ ββ β = π£π΄π΅ββ ββ ββ β + π£π΅πΆββ ββ ββ β ππ΄π΅ββ ββ ββ β = ππ΅π΄ββββββββ
4.44 4.45
Uniform Circular Motion
π =π£2
π π =
2ππ
π£ 4.34
4.35
Chapter 5
Chapter 6
Newtonβs Second Law
General οΏ½βοΏ½πππ‘ = ποΏ½βοΏ½
5.1
Component form
πΉπππ‘,π₯ = πππ₯ πΉπππ‘,π¦ = πππ¦
πΉπππ‘,π§ = πππ¦
5.2
Gravitational Force
Gravitational Force
πΉπ = ππ 5.8
Weight
π = ππ 5.12
Friction Static Friction (maximum)
ππ ,πππ₯ = ππ πΉπ 6.1
Kinetic Frictional ππ = πππΉπ 6.2
Drag Force π· =1
2πΆππ΄π£2 6.14
Terminal velocity π£π‘ = β2πΉπ
πΆππ΄ 6.16
Centripetal acceleration
π =π£2
π 6.17
Centripetal Force
πΉ =ππ£2
π 6.18
Chapter 7
Chapter 8
Kinetic Energy
πΎ =1
2ππ£2 7.1
Work done by constant Force
π = πΉππππ π = οΏ½βοΏ½ β π 7.7 7.8
Work- Kinetic Energy Theorem
βπΎ = πΎπ β πΎ0 = π 7.10
Work done by gravity
ππ = ππππππ π 7.12
Work done by lifting/lowering object
βπΎ = ππ + ππ
ππ = πππππππ πΉππππ 7.15
Spring Force (Hookeβs law)
οΏ½βοΏ½π = βππ πΉπ₯ = βππ₯ (along x-axis)
7.20 7.21
Work done by spring ππ =1
2ππ₯π
2 β1
2ππ₯π
2 7.25
Work done by Variable Force
π = β« πΉπ₯ππ₯π₯π
π₯π
+ β« πΉπ¦ππ¦π¦π
π¦π
+ β« πΉπ§ππ§π§π
π§π
7.36
Average Power (rate at which that force does work on an object)
πππ£π =π
βπ‘ 7.42
Instantaneous Power π =ππ
ππ‘= πΉππππ π = οΏ½βοΏ½ β οΏ½βοΏ½
7.43 7.47
Potential Energy βπ = βπ = β β« πΉ(π₯)ππ₯π₯π
π₯π
8.1 8.6
Gravitational Potential Energy
βπ = ππβπ¦ 8.7
Elastic Potential Energy π(π₯) =1
2ππ₯2 8.11
Mechanical Energy πΈπππ = πΎ + π 8.12
Principle of conservation of mechanical energy
πΎ1 + π1 = πΎ2 + π2 πΈπππ = βπΎ + βπ = 0
8.18 8.17
Force acting on particle πΉ(π₯) = βππ(π₯)
ππ₯ 8.22
Work on System by external force With no friction
π = βπΈπππ = βπΎ + βπ 8.25 8.26
Work on System by external force With friction
π = βπΈπππ + βπΈπ‘β 8.33
Change in thermal energy
βπΈπ‘β = ππππππ π 8.31
Conservation of Energy *if isolated W=0
π = βπΈ = βπΈπππ + βπΈπ‘β + βπΈπππ‘ 8.35
Average Power πππ£π =βπΈ
βπ‘ 8.40
Instantaneous Power π =ππΈ
ππ‘ 8.41
**In General Physics, Kinetic Energy is abbreviated to KE and Potential Energy is PE
Chapter 9
Impulse and Momentum
Impulse π½ = β« οΏ½βοΏ½(π‘)ππ‘
π‘π
π‘π
π½ = πΉπππ‘βπ‘
9.30 9.35
Linear Momentum οΏ½βοΏ½ = ποΏ½βοΏ½ 9.22
Impulse-Momentum Theorem
π½ = ΞοΏ½βοΏ½ = οΏ½βοΏ½π β οΏ½βοΏ½π 9.31 9.32
Newtonβs 2nd law οΏ½βοΏ½πππ‘ =ποΏ½βοΏ½
ππ‘ 9.22
System of Particles
οΏ½βοΏ½πππ‘ = ποΏ½βββοΏ½πππ
οΏ½ββοΏ½ = ποΏ½βοΏ½πππ
οΏ½βοΏ½πππ‘ =ποΏ½βββοΏ½
ππ‘
9.14 9.25 9.27
Collision
Final Velocity of 2 objects in a head-on collision where one object is initially at rest 1: moving object 2: object at rest
π£1π = (π1 β π2
π1 + π2) π£1π
π£2π = (2π1
π1 + π2) π£1π
9.67 9.68
Conservation of Linear Momentum (in 1D)
οΏ½ββοΏ½ = ππππ π‘πππ‘
οΏ½ββοΏ½π = οΏ½ββοΏ½π
9.42 9.43
Elastic Collision
οΏ½βοΏ½1π + οΏ½βοΏ½2π = οΏ½βοΏ½1π + οΏ½βοΏ½2π
π1π£π1 + π2π£12 = π1π£π1 + π2π£π2
πΎ1π + πΎ2π = πΎ1π + πΎ2π
9.50 9.51 9.78
Collision continuedβ¦
Inelastic Collision π1π£01 + π2π£02 = (π1 + π2)π£π
Conservation of Linear Momentum (in 2D)
οΏ½ββοΏ½1π + οΏ½ββοΏ½2π = οΏ½ββοΏ½1π + οΏ½ββοΏ½2π
9.77
Average force πΉππ£π = β
π
βπ‘βπ = β
π
βπ‘πβπ£
πΉππ£π = ββπ
βπ‘βπ£
9.37 9.40
Center of Mass
Center of mass location ππππ =1
πβ ππ
π
π=1
ππ 9.8
Center of mass velocity οΏ½βοΏ½πππ =1
πβ ππ
π
π=1
οΏ½βοΏ½π
Rocket Equations
Thrust (Rvrel)
π π£πππ = ππ
9.88
Change in velocity
Ξπ£ = π£πππππππ
ππ 9.88
Chapter 10
Angular displacement (in radians
π =π
π
Ξπ = π2 β π1
10.1 10.4
Average angular velocity πππ£π =
βπ
βπ‘ 10.5
Instantaneous Velocity π =ππ
ππ‘ 10.6
Average angular acceleration πΌππ£π =
βπ
βπ‘ 10.7
Instantaneous angular acceleration πΌ =
ππ
ππ‘ 10.8
Rotational Kinematics
π = π0 + πΌπ‘ 10.12
Ξπ = π0π‘ +1
2πΌπ‘2 10.13
π2 = π02 + 2πΌΞπ 10.14
Ξπ =1
2(π + π0)π‘ 10.15
Ξπ = ππ‘ β1
2πΌπ‘2 10.16
Relationship Between Angular and Linear Variables
Velocity π£ = ππ 10.18
Tangential Acceleration ππ‘ = πΌπ 10.19
Radical component of οΏ½βοΏ½ ππ =π£2
π= π2π 10.23
Period π =2ππ
π£=
2π
π
10.19 10.20
Rotation inertia πΌ = β ππππ2 10.34
Rotation inertia (discrete particle system)
πΌ = β« π2ππ 10.35
Parallel Axis Theorem h=perpendicular distance between two axes
πΌ = πΌπππ + πβ2 10.36
Torque π = ππΉπ‘ = πβ₯πΉ = ππΉπ πππ 10.39- 10.41
Newtonβs Second Law ππππ‘ = πΌπΌ 10.45
Rotational work done by a toque
π = β« πππππ
ππ
π = πβπ (π constant)
10.53 10.54
Power in rotational motion
π =ππ
ππ‘= ππ 10.55
Rotational Kinetic Energy
πΎ =1
2πΌπ2 10.34
Work-kinetic energy theorem βπΎ = πΎπ β πΎπ =
1
2πΌππ
2 β1
2πΌππ
2 = π 10.52
Moments of Inertia I for various rigid objects of Mass M
Thin walled hollow cylinder or hoop about central axis
πΌ = ππ 2
Annular cylinder (or ring) about central axis
πΌ =1
2π(π 1
2 + π 22)
Solid cylinder or disk about central axis
πΌ =1
2ππ 2
Solid cylinder or disk about central diameter
πΌ =1
4ππ 2 +
1
12ππΏ2
Solid Sphere, axis through center
πΌ =2
5ππ 2
Solid Sphere, axis tangent to surface
πΌ =7
5ππ 2
Thin Walled spherical shell, axis through center
πΌ =2
3ππ 2
Thin rod, axis perpendicular to rod and passing though center
πΌ =1
12ππΏ2
Thin rod, axis perpendicular to rod
and passing though end
πΌ =1
3ππΏ2
Thin Rectangular sheet (slab), axis parallel to sheet and passing though
center of the other edge
πΌ =1
12ππΏ2
Thin Rectangular sheet (slab_, axis along one edge
πΌ =1
3ππΏ2
Thin rectangular sheet (slab) about perpendicular axis through center
πΌ =1
12π(π2 + π2)
Chapter 11
Rolling Bodies (wheel)
Speed of rolling wheel π£πππ = ππ 11.2
Kinetic Energy of Rolling Wheel πΎ =
1
2πΌππππ2 +
1
2ππ£πππ
2 11.5
Acceleration of rolling wheel
ππππ = πΌπ 11.6
Acceleration along x-axis extending up the ramp
ππππ,π₯ = βππ πππ
1 +πΌπππ
ππ 2
11.10
Torque as a vector
Torque π = π Γ οΏ½βοΏ½ 11.14
Magnitude of torque π = ππΉβ₯ = πβ₯πΉ = ππΉπ πππ 11.15-11.17
Newtonβs 2nd Law ππππ‘ =πβββ
ππ‘ 11.23
Angular Momentum
Angular Momentum π£ββββ = οΏ½ββοΏ½ Γ οΏ½βββοΏ½ = π(οΏ½ββοΏ½ Γ οΏ½βββοΏ½) 11.18
Magnitude of Angular Momentum
β = πππ£π πππ β = ππβ₯ = πππ£β₯
11.19-11.21
Angular momentum of a system of particles
οΏ½ββοΏ½ = β βββπ
π
π=1
ππππ‘ =ποΏ½ββοΏ½
ππ‘
11.26 11.29
Angular Momentum continued
Angular Momentum of a rotating rigid body
πΏ = πΌπ 11.31
Conservation of angular momentum
οΏ½ββοΏ½ = ππππ π‘πππ‘
οΏ½ββοΏ½π = οΏ½ββοΏ½π
11.32 11.33
Precession of a Gyroscope
Precession rate Ξ© =πππ
πΌπ 11.31
Chapter 12
Chapter 13
Static Equilibrium
οΏ½βοΏ½πππ‘ = 0 12.3
ππππ‘ = 0 12.5
If forces lie on the xy-plane
οΏ½βοΏ½πππ‘,π₯ = 0, οΏ½βοΏ½πππ‘,π¦ = 0 12.7 12.8
ππππ‘,π§ = 0 12.9
Stress (force per unit area) Strain (fractional change in length)
π π‘πππ π = ππππ’ππ’π Γ π π‘ππππ 12.22
Stress (pressure) π =πΉ
π΄
Tension/Compression E: Youngβs modulus
πΉ
π΄= πΈ
βπΏ
πΏ 12.23
Shearing Stress G: Shear modulus
πΉ
π΄= πΊ
βπ₯
πΏ 12.24
Hydraulic Stress B: Bulk modulus π = π΅
βπ
π
Gravitational Force (Newtonβs law of gravitation)
πΉ = πΊπ1π2
π2 13.1
Principle of Superposition
οΏ½βοΏ½1,πππ‘ = β οΏ½βοΏ½1π
π
π=2
13.5
Gravitational Force acting on a particle from an extended body
οΏ½βοΏ½1 = β« ποΏ½βοΏ½ 13.6
Gravitational acceleration ππ =
πΊπ
π2 13.11
Gravitation within a spherical Shell πΉ =
πΊππ
π 3π 13.19
Gravitational Potential Energy π = β
πΊππ
π 13.21
Potential energy on a system (3 particles)
π = β (πΊπ1π2
π12+
πΊπ1π3
π13+
πΊπ2π3
π23) 13.22
Escape Speed π£ = β2πΊπ
π 13.28
Keplerβs 3rd Law (law of periods)
π2 = (4π2
πΊπ) π3 13.34
Energy for bject in circular orbit
π = βπΊππ
π πΎ =
πΊππ
2π
13.21 13.38
Mechanical Energy (circular orbit)
πΈ = βπΊππ
2π 13.40
Mechanical Energy (elliptical orbit)
πΈ = βπΊππ
2π 13.42
*Note: πΊ = 6.6704 Γ 10β11 π β π2/ππ2
Chapter 14
Chapter 15
Density π =
βπ
βπ
π =π
π
14.1 14.2
Pressure π =
βπΉ
βπ΄
π =πΉ
π΄
14.3 14.4
Pressure and depth in a static Fluid P1 is higher than P2
π2 = π1 + ππ(π¦1 β π¦2) π = π0 + ππβ
14.7 14.8
Gauge Pressure ππβ
Archimedesβ principle πΉπ = πππ 14.16
Mass Flow Rate π π = ππ π = ππ΄π£ 14.25
Volume flow rate π π = π΄π£ 14.24
Bernoulliβs Equation π +1
2ππ£2 + πππ¦ = ππππ π‘πππ‘ 14.29
Equation of continuity π π = ππ π = ππ΄π£ = ππππ π‘πππ‘ 14.25
Equation of continuity when
π π = π΄π£ = ππππ π‘πππ‘ 14.24
Frequency cycles per time
π =1
π 15.2
displacement π₯ = π₯πcos (ππ‘ + π) 15.3
Angular frequency π =2π
π= 2ππ 15.5
Velocity π£ = βππ₯πsin(ππ‘ + π) 15.6
Acceleration π = βπ2π₯πcos (ππ‘ + π) 15.7
Kinetic and Potential Energy πΎ =
1
2ππ£2 π =
1
2ππ₯2
Angular frequency π = βπ
π 15.12
Period π = 2πβπ
π 15.13
Torsion pendulum π = 2πβπΌ
π 15.23
Simple Pendulum π = 2πβπΏ
π 15.28
Physical Pendulum π = 2πβπΌ
πππΏ 15.29
Damping force οΏ½βοΏ½π = βποΏ½βοΏ½
displacement π₯(π‘) = π₯ππβππ‘
2πcos (πβ²π‘ + π) 15.42
Angular frequency πβ² = βπ
πβ
π2
4π2 15.43
Mechanical Energy πΈ(π‘) β1
2ππ₯π
2 πβππ‘π 15.44
Chapter 16
Sinusoidal Waves
Mathematical form (positive direction)
π¦(π₯, π‘) = π¦πsin (ππ₯ β ππ‘) 16.2
Angular wave number π =2π
π 16.5
Angular frequency π =2π
π= 2ππ 16.9
Wave speed π£ =π
π=
π
π= ππ 16.13
Average Power πππ£π =1
2ππ£π2π¦π
2 16.33
Traveling Wave Form π¦(π₯, π‘) = β(ππ₯ Β± ππ‘) 16.17
Wave speed on stretched string
π£ = βπ
π 16.26
Resulting wave when 2 waves only differ by phase constant
π¦β²(π₯, π‘) = [2π¦π cos (1
2π)] sin (ππ₯ β ππ‘ +
1
2π) 16.51
Standing wave π¦β²(π₯, π‘) = [2π¦π sin(ππ₯)]cos (ππ‘) 16.60
Resonant frequency π =π£
π= π
π£
2πΏ for n=1,2,β¦ 16.66
Chapter 17
Sound Waves
Speed of sound wave π£ = βπ΅
π 17.3
displacement π = π πcos (ππ₯ β ππ‘) 17.12
Change in pressure Ξπ = Ξππ sin(ππ₯ β ππ‘) 17.13
Pressure amplitude Ξππ = (π£ππ)π π 17.14
Interference
Phase difference π =ΞπΏ
π2π 17.21
Fully Constructive Interference
π = π(2π) for m=0,1,2β¦ ΞπΏ
π= 0,1,2
17.22 17.23
Full Destructive interference
π = (2π + 1)π for m=0,12 ΞπΏ
π= .5,1.5,2.5 β¦
17.24 17.25
Mechanical Energy πΈ(π‘) β1
2ππ₯π
2 πβππ‘π 15.44
Sound Intensity
Intensity πΌ =
π
π΄
πΌ =1
2ππ£π2π π
2
17.26 17.27
Intensity -uniform in all directions
πΌ =ππ
4ππ2 17.29
Intensity level in
decibels π½ = (10ππ΅) log (
πΌ
πΌπ) 17.29
Mechanical Energy πΈ(π‘) β1
2ππ₯π
2 πβππ‘π 15.44
Standing Waves Patterns in Pipes
Standing wave frequency (open at both ends)
π =π£
π=
ππ£
2πΏ for n=1,2,3 17.39
Standing wave frequency (open at one end)
π =π£
π=
ππ£
4πΏ for n=1,3,5 17.41
beats πππππ‘ = π1 β π2 17.46
Doppler Effect
Source Moving toward stationary observer
πβ² = ππ£
π£ β π£π 17.53
Source Moving away from stationary observer
πβ² = ππ£
π£ + π£π 17.54
Observer moving toward stationary source
πβ² = ππ£ + π£π·
π£ 17.49
Observer moving away from stationary source
πβ² = ππ£ β π£π·
π£ 17.51
Shockwave
Half-angle π of Mach cone
π πππ =π£
π£π 17.57
Chapter 18
Temperature Scales
Fahrenheit to Celsius ππΆ =5
9(ππΉ β 32) 18.8
Celsius to Fahrenheit ππΉ =9
5ππΆ + 32 18.8
Celsius to Kelvin π = ππΆ + 273.15 18.7
Thermal Expansion
Linear Thermal Expansion βπΏ = πΏπΌβπ 18.9
Volume Thermal Expansion βπ = ππ½βπ 18.10
Heat
Heat and temperature change
π = πΆ(ππ β ππ)
π = ππ(ππ β ππ)
18.13 18.14
Heat and phase change π = πΏπ 18.16
Power P=Q/t
Power (Conducted) πππππ =π
π‘= ππ΄
ππ» β ππΆ
πΏ 18.32
Rate objects absorbs energy
ππππ = πππ΄ππππ£4 18.39
Power from radiation ππππ = πππ΄π4 18.38
π = 5.6704 Γ 10β8 π/π2 β πΎ4
First Law of Thermodynamics
First Law of Thermodynamics
βπΈπππ‘ = πΈπππ‘,π β πΈπππ‘,π = π β π
ππΈπππ‘ = ππ β ππ
18.26 18.27
Note: βπΈπππ‘ Change in Internal Energy Q (heat) is positive when the system absorbs heat and negative when it loses heat. W (work) is work done by system. W is positive when expanding and negative contracts because of an external force
Applications of First Law
Adiabatic (no heat flow)
Q=0 βπΈπππ‘ = βπ
(constant volume) W=0
βπΈπππ‘ = π
Cyclical process βπΈπππ‘ = 0
Q=W
Free expansions π = π = βπΈπππ‘ = 0
Misc.
Work Associated with Volume Change
π = β« ππ = β« πππππ
ππ
π = πβπ£
18.25
Revised 7/20/17