Formelsamling PDF

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Summary

Formelsamling till kursen termodynamik...

Description

 L  L0  T

 linear thermal expansion

 V   V0  T

 volume thermal expansion

Q  mc T

 heat required to change temperature of a certain mass

Q  nC T

 heat required to change temperature of a certain number of moles

Q   mL

H

𝐻=

 heat transfer in a phase change

dQ T T  kA H C dt L 𝐴(𝑇𝐻−𝑇𝐶 ) 𝑅

 heat current in conduction 

(heat current in conduction)

𝐿

𝑅 = 𝑘 (relationship between thermal resistance and thermal conductivity)

 heat current in radiation

H  Ae T 4

4 4 Hnet  Ae  T  Ts 

(net heat current in radiation)

mtotal  nM

 total mass, number of moles, and molar mass

pV  nRT

ideal-gas equation

(𝑝 +

𝑎 𝑛2 ) (𝑉 𝑉2

− 𝑛 𝑏 ) = 𝑛 𝑅 𝑇 (van der Waals’ equation)

𝑅 = 𝑘 𝑁𝐴 (gas constant, Boltzmann constant, Avogadro’s number)

M  NA m 𝐸𝑘𝑖𝑛 =

𝑚 𝑣2 2

molar mass, Avogadro's number, and mass of a molecule 𝑝2

= 2𝑚 (kinetic energy)

𝑝 = 𝑚 𝑣 (momentum)

𝐸𝑝𝑜𝑡 = 𝑚 𝑔 ℎ (potential energy near the earth’s surface) 𝑊 = 𝐹 𝑠 (work)

 average translational kinetic energy of an ideal gas

3

Ktr  nRT 2

1 2

m  2  av  3 kT

average translational kinetic energy of a gas molecule 

2

 

 rms 

2

   t mean 

av

3kT 3RT  m M



V 4 2r 2N

 root-mean-square speed of a gas molecule

 mean free path of a gas molecule

CV  3 R

ideal gas of point particles 

CV  5 R

diatomic gas, including rotation 

CV  3R

 ideal monatomic solid

2

2

3/ 2

2  m  f    4   2e m / 2 kT   2  kT 

V2

 work done in a volume change 

W   p dV V1

W  p V2  V1 

U  Q  W

Maxwell  Boltzmann distribution 

 work done in a volume change at constant pressure

 first law of thermodynamics

dU  dQ  dW

first law of thermodynamics, infinitesimal process

𝑑𝑈 = 𝑛 𝐶𝑉 𝑑𝑇 (change of inner energy and temperature for ideal gas, all processes) Cp  CV  R

 molar heat capacities of an ideal gas



Cp CV

ratio of heat capacities

W  nCV T1  T2 

W

adiabatic process, ideal gas 

1 CV pV  pV  pV  p V  1 1  2 2  1 1 1 2 2 R

 adiabatic process, ideal gas

𝑝 𝑉  = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (reversible, adiabatic process) 𝑇 𝑉 −1 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (reversible, adiabatic process)

e

W Q Q  1 C  1 C QH QH QH

K

QC W

e Carnot  1 

KCarnot 

S  

2

1

QC Q H  QC



TC TH  TC  TH TH

TC TH  TC dQ T

S  k ln w

 thermal efficiency of an engine

 coefficient of performance of a refrigerator  efficiency of a Carnot engine

 coefficient of performance of a Carnot refrigerator

entropy change in a reversible process 

 microscopic expression for entropy...