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Physics 4b Formula Sheet 17-21

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Chapter 17

9 TF  TC  32 5 TC  5 TF  32 9

(17.1)

(17.2)

TK  TC  273.15

(17.3)

T2 p2  T1 p1

 constant-volume gas thermometer, T
L  L0 T
V   V0 T

in kelvins 

(17.4)

 linear thermal expansion  for solids
 volume thermal expansion  for liquids of mass m

(17.6) (17.12) (17.13) (17.18) (17.20)

Q  mc T Q  nC T

 heat required for temperature change T

 heat required for temperature change of n moles  heat transfer in a phase change
������ ������������ = 0 for an isolated system.

Q   mL

H

T T dQ  kA H C dt L

 heat current in conduction 

������ = ������ Σ (������ /������ ) when there are several layers.
������ ������ ������

������

H  Ae T 4

 heat current in radiation 

(17.25)

H net  Ae T 4  Ae Ts 4  Ae T 4  Ts 4 

(17.26)

Copyright © 2012 Pearson Education, Inc.

Page 1 of 7

Chapter 18 mtotal  nM

 total mass, number of moles, and molar mass pV  nRT

(18.2) (18.3) (18.8)

 ideal-gas equation 

M  NAm

 molar mass, Avogadro’s number, and mass of a molecule

K tr 

3 nRT 2 

 average translational kinetic energy of n moles of ideal gas
3 kT 2

(18.14)

1 m 2 2

 

av

 average translational kinetic energy of a gas molecule
 root-mean-square speed of a gas molecule

(18.16)

rms 

 
2

av



3kT 3RT  m M

(18.19)

   tmean 

V 4 2r 2 N

 mean free path of a gas molecule 

(18.21)

CV 

3 R 2

 ideal gas of point particles 

(18.25)

CV 

5 R 2

 diatomic gas, including rotation 
 ideal monatomic solid 
3/ 2

(18.26)

CV  3R

(18.28)

 m  f    4    2 kT 

 2e m

2

/ 2 kT

 Maxwell  Boltzmann distribution 

Copyright © 2012 Pearson Education, Inc.

Page 2 of 7

Chapter 19

W   p dV
V2 V1

 work done in a volume change

(19.2)

W  p V2  V1 

 work done in a volume change at constant pressure
 first law of thermodynamics

(19.3) (19.4) (19.6) (19.17)

U 2  U1  U  Q  W dU  dQ  dW

 first law of thermodynamics, infinitesimal process

C p  CV  R

 molar heat capacities of an ideal gas
Cp CV



 ratio of heat capacities

(19.18)

Isochoric Process: ������ = 0 ������ = ������������������ ������ =
������������ ������

������������ = ������,

������������ ������������

= ������������
������

������

Isobaric process: ������������ ������������, ������ ������������ ������������, ������ ������������ ������������ = ������������ ������������

������ = ������������,

������ = ������������������ ������ =

������ = ������������������ ������ =

Isothermal Process: ������ = ������ = ������������������ln ( ������������ ) ,
������

������

������ = 0,

������������ ������������ = ������������ ������������

Adiabatic Process: ������ = −Δ������ = −������������������ Δ������ = −
������������ ������

(������������ ������������ − ������������ ������������ ), ������ = 0, ������������ ������������ = ������������ ������ , ������������ ������������ ������

������

������

������−1

= ������������ ������ ������

������−1

Copyright © 2012 Pearson Education, Inc.

Page 3 of 7

Cycle: ������ = ������ = ������������������������ ������������������������������������������ ������������ ������ℎ������ ������������������������������, Δ������ = 0 Chapter 20
Q Q W  1 C  1 C QH QH QH

e

 thermal efficiency of an engine

(20.4)

e  1

1 r  1

 thermal efficiency in Otto cycle
 coefficient of performance of a refrigerator 
|������������ | |������������ | = |������| |������������ | − |������������ |

(20.6)

K

QC QC  W QH  QC

������ℎ������������������−������������������������ =

eCarnot  1 

TC TH  TC  TH TH

 efficiency of a Carnot engine

(20.14)

K Carnot 

TC TH  TC

 coefficient of performance of a Carnot refrigerator  dQ T

(20.15)

S  

2

1

 entropy change in a reversible process
When T is constant (reversible process)
������ ������

(20.19)

������ =

������ ������

������ = ������������������ ln ( ������������ ) + ������������ ln ( ������������ ) (reversible process)
������ ������

Copyright © 2012 Pearson Education, Inc.

Page 4 of 7

Chapter 21

F

1 q1q2 4 0 r 2 F0 q0

(Coulomb’s law: force between two point charges)

(21.2)

E

(definition of electric field as electric force per unit charge)

(21.3)

E 

1 q rˆ (electric field of a point charge) 4 0 r 2
⃗ ������+������ ������ ⃗ ������������������������������������������

Dipole Field

⃗ ������−������ ������ ≫ ������ ⇒ ⃗ ������������������������������������������ = −������
������ ������ 3

������

+������ ������

−������

Copyright © 2012 Pearson Education, Inc.

Page 5 of 7

������ ≫ ������



⃗ ������ = 2������

������ ������ 3

������

Electric field due to a very long wire with linear charge density ������.

⃗ ������ =
Let

������������������ ������������ = ������ ������̂ ������ ������√(������2 + ������2 /4)

������ → ∞ 2������ ⃗ ������ = ������ ������̂ ������

Electric Field due to a uniform ring charge.

⃗ ������ = ������

������������ ������̂ (������ 2 + ������2 )3/2

Copyright © 2012 Pearson Education, Inc.

Page 6 of 7

Electric Field due to uniform disk charge.

⃗ ������ = 2������������������ (1 −

1 √(������ 2 /������ 2 + 1)

) ������̂

������ → ∞



⃗ ������ = 2������������������ =

������ 2������0

������̂

������ = ������ℎ������������������������/������������������������ Electric Dipole in a uniform electric Field:

  pE sin  (magnitude of the torque on an electric dipole)
  p E
(torque on an electric dipole, in vector form)

(21.15) (21.16)

⃗ ������ = −������. ������ (potential energy of an electric dipole in a uniform electric field)

Copyright © 2012 Pearson Education, Inc.

Page 7 of 7

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